diff options
| author | Sven Eisenhauer <sven@sven-eisenhauer.net> | 2023-11-10 15:11:48 +0100 |
|---|---|---|
| committer | Sven Eisenhauer <sven@sven-eisenhauer.net> | 2023-11-10 15:11:48 +0100 |
| commit | 33613a85afc4b1481367fbe92a17ee59c240250b (patch) | |
| tree | 670b842326116b376b505ec2263878912fca97e2 /Bachelor/Numerische Mathematik/Num05Aufg3.nb | |
| download | Studium-33613a85afc4b1481367fbe92a17ee59c240250b.tar.gz Studium-33613a85afc4b1481367fbe92a17ee59c240250b.tar.bz2 | |
Diffstat (limited to 'Bachelor/Numerische Mathematik/Num05Aufg3.nb')
| -rw-r--r-- | Bachelor/Numerische Mathematik/Num05Aufg3.nb | 2655 |
1 files changed, 2655 insertions, 0 deletions
diff --git a/Bachelor/Numerische Mathematik/Num05Aufg3.nb b/Bachelor/Numerische Mathematik/Num05Aufg3.nb new file mode 100644 index 0000000..a591124 --- /dev/null +++ b/Bachelor/Numerische Mathematik/Num05Aufg3.nb @@ -0,0 +1,2655 @@ +(************** Content-type: application/mathematica **************
+ CreatedBy='Mathematica 5.0'
+
+ Mathematica-Compatible Notebook
+
+This notebook can be used with any Mathematica-compatible
+application, such as Mathematica, MathReader or Publicon. The data
+for the notebook starts with the line containing stars above.
+
+To get the notebook into a Mathematica-compatible application, do
+one of the following:
+
+* Save the data starting with the line of stars above into a file
+ with a name ending in .nb, then open the file inside the
+ application;
+
+* Copy the data starting with the line of stars above to the
+ clipboard, then use the Paste menu command inside the application.
+
+Data for notebooks contains only printable 7-bit ASCII and can be
+sent directly in email or through ftp in text mode. Newlines can be
+CR, LF or CRLF (Unix, Macintosh or MS-DOS style).
+
+NOTE: If you modify the data for this notebook not in a Mathematica-
+compatible application, you must delete the line below containing
+the word CacheID, otherwise Mathematica-compatible applications may
+try to use invalid cache data.
+
+For more information on notebooks and Mathematica-compatible
+applications, contact Wolfram Research:
+ web: http://www.wolfram.com
+ email: info@wolfram.com
+ phone: +1-217-398-0700 (U.S.)
+
+Notebook reader applications are available free of charge from
+Wolfram Research.
+*******************************************************************)
+
+(*CacheID: 232*)
+
+
+(*NotebookFileLineBreakTest
+NotebookFileLineBreakTest*)
+(*NotebookOptionsPosition[ 88646, 2521]*)
+(*NotebookOutlinePosition[ 89370, 2546]*)
+(* CellTagsIndexPosition[ 89326, 2542]*)
+(*WindowFrame->Normal*)
+
+
+
+Notebook[{
+Cell[BoxData[
+ StyleBox[\( (*\ \ \ \ \ Numerik\ : \ \ Aufgabe\ \
+3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ S\
+S\ \ 2005\ \ \ *) \),
+ "Subtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Off[General::spell]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ StyleBox[\(\(\ \ \ \ \ \ \)\(\ \)\(\ \)\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Stellenzahl",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["die",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Eingabematrix",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["vorgeben",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["ipl",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["=",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["1",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[",",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["2",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[",",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["3",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[",",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[\(4\ \ oder\ 5\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{\(ipl\ = \ 1;\), "\n", " ",
+ RowBox[{\(stlist\ = \ {\ 8, \ 12, \ 16, \ 20, 24\ }\), ";",
+ " ",
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[1, 1, 0]],
+ StyleBox[" ",
+ Background->RGBColor[1, 1, 0]],
+ StyleBox[\(Liste\ der\ vorgegebenen\ Stellenzahlen\),
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[1, 1, 0]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[1, 1, 0]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[1, 1, 0]]}], "\n",
+ " ", \(st = \ stlist[\([ipl]\)]\), ";", " "}]}]}]], "Input"],
+
+Cell[BoxData[
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ Berechnung\ der\ inversen\ Matrix\ zur\ \
+Hilbertmatrix\ H\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \( (*\ \ \ \ \ \ Rechengenauigkeit\ gen\ \(festlegen\ !\)\ \ Standard\ \
+ist\ gen\ = \ 16\ \ \ \ *) \)], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(\($MinPrecision = \($MaxPrecision = \(gen =
+ 28\)\);\)\(\ \ \ \)\)\)], "Input"],
+
+Cell[BoxData[
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ Bereitstellen\ der\ Fakult\
+\[ADoubleDot]t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Fakul[k_] := Fakul[k - 1]*k\ \ ; \ \ Fakul[0] = 1. ;\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]], " "}]],
+ StyleBox[\(Funktionsunterprogramm\ zum\ Runden\ auf\ L\ Stellen\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(Runden[xN_,
+ L_]\)\(:=\)\(\ \)\((\ \ signum =
+ If[xN\ < 0, \ SetPrecision[\(-1. \), gen],
+ SetPrecision[1.0, gen]];
+ zehn = SetPrecision[10.0, gen]; \[IndentingNewLine]expo =
+ If[\ Abs[xN] < 1, L - IntegerPart[Log[10. , Abs[xN]]],
+ L - IntegerPart[Log[10. , Abs[xN]]] - 1]; \[IndentingNewLine]xL =
+ If[xN == 0, 0. ,
+ signum*Floor[
+ Abs[xN]*zehn\^expo + SetPrecision[0.5, gen] +
+ zehn\^\((L - gen)\)]*zehn\^\(-expo\)];
+ xL)\)\(\t\)\)\)], "Input"],
+
+Cell[BoxData[
+ \(PaddedForm[Runden[1/3, 18], {gen, 19}]\)], "Input"],
+
+Cell[BoxData[
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ Bereitstellen\ der\ Zeilensummen -
+ Norm\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(NormMat[matrix_, n_] := \ \ \((\
+ Do[zeisum[matrix, i,
+ n] = \ \[Sum]\+\(j = 1\)\%n Abs[matrix[i, j]], {i, 1, n}]\ ;
+ zwimax = zeisum[matrix, 1, n];
+ Do[zwimax = Max[zwimax, zeisum[matrix, i, n]], {i, 2, n}];
+ zwimax\ )\)\)], "Input"],
+
+Cell[BoxData[
+ StyleBox[\( (*\ \ \ \ \
+Erstellen\ \ einer\ \ Liste\ \ von\ \ vorgegebenen\ \ Ordnungen\ n\ \ der\ \
+Matrizen\ nach\ Hilbert\ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(nlist = {3, 5, 7, 9, 11, 13, 15, 17, 19};\)\(\ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["Erstellen",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["der",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["Hilbertmatrix",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["Hplus",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["mit",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["gen",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]], " ",
+ StyleBox["Stellen",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{n = nlist[\([l]\)], \n
+ Do[Do[Htabplus[l, i, j] = \(Hplus[i, j] =
+ SetPrecision[1/\((i + j - 1)\), gen]\), {i, 1,
+ nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}]]}, \t{l, 1,
+ 9}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ RowBox[{
+ RowBox[{
+ StyleBox["Test",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["-",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle"],
+ StyleBox[\(Ausgabe\ der\ \ Hilbertmatrix\ \ Htabplus\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["=",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ RowBox[{
+ RowBox[{
+ StyleBox["Hplus",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["und",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["\[IndentingNewLine]",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["ihrer",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["intern",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["berechneten",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Inversen",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Hinvplus",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["e",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["i",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["n",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["e",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["n",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Wert",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox["=",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["lfest",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 3;\)\[IndentingNewLine]
+ Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\[IndentingNewLine]
+ TableForm[
+ Table[ScientificForm[
+ PaddedForm[Htabplus[l, i, j]\ , {gen, gen - 1}]], {l, lfest,
+ lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \)\)\)], "Input"],
+
+Cell[BoxData[
+ \(\(Hmatplus[lfest] =
+ Table[Htabplus[lfest, i, j], {i, 1, nlist[\([lfest]\)]}, {j, 1,
+ nlist[\([lfest]\)]}\ ];\)\)], "Input"],
+
+Cell[BoxData[{
+ \(Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\), "\[IndentingNewLine]",
+ \(Hmatplus[lfest] // MatrixForm\)}], "Input"],
+
+Cell[BoxData[
+ \(\(Hinvplus = Inverse[Hmatplus[lfest]];\)\)], "Input"],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 3;\)\t\n
+ Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\[IndentingNewLine]
+ TableForm[
+ Table[ScientificForm[
+ PaddedForm[Hinvplus[\([i, j]\)]\ , {gen, gen - 1}]], {l, lfest,
+ lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["Erstellen",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["der",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["Hilbertmatrix",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["H",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["mit",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["st",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Stellen",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ \ \
+Gleichzeitig\ \ werden\ \ alle\ \ Normen\ \ von\ \ H\ \ \(b
+ erechnet\)\ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{n = nlist[\([l]\)], \n
+ Do[Do[Htab[l, i, j] = \(H[i, j] =
+ Runden[Htabplus[l, i, j], st]\)\ , {i, 1,
+ nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}]], \[IndentingNewLine]\
+ NormHil[l] = NormMat[H, n]}, {l, 1, 9}]\)], "Input"],
+
+Cell[BoxData[
+ StyleBox[\(\( (*\ \ \ \ \ \ \ Ausgabe\ \ der\ \ Hilbertmatrix\ \ Htab\ = \
+\ \(H\ \ \ und\ \[IndentingNewLine]
+ \ \ \ \ \ \ ihrer\ \ intern\ \ berechneten\ \ Inversen\ \ \ Hinv\ \ f\
+\[UDoubleDot]r\ \ e\ i\ n\ e\ n\ \ Wert\ \ von\ \ nlist =
+ lfest\)\ \ \ \ \ \ \ *) \)\(\ \ \)\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 8;\)\ \ \ \ \ \ \[IndentingNewLine]
+ Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\[IndentingNewLine]
+ TableForm[
+ Table[ScientificForm[PaddedForm[Htab[l, i, j]\ , {st, st - 1}]], {l,
+ lfest, lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \ \ \ \ \ \)\)\)], "Input"],
+
+Cell[BoxData[
+ \(\(Hmat[lfest] =
+ Table[Htab[lfest, i, j], {i, 1, nlist[\([lfest]\)]}, {j, 1,
+ nlist[\([lfest]\)]}\ ];\)\)], "Input"],
+
+Cell[BoxData[{
+ \(Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\ \ \), "\[IndentingNewLine]",
+ \(\ Hmat[lfest] // MatrixForm\)}], "Input"],
+
+Cell[BoxData[
+ \(\(Hinv = Inverse[Hmat[lfest]];\)\)], "Input"],
+
+Cell[BoxData[
+ \(\(\(Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\[IndentingNewLine]
+ TableForm[
+ Table[ScientificForm[PaddedForm[Hinv[\([i, j]\)]\ , {st, st - 1}]], {l,
+ lfest, lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox[\(Erstellen\ der\ Differenzmatrix\ \ Hplus\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["-",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["H",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]], " ",
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\(\(\ \ \ \)\(\ \)\(\ \ \)\)
+ Gleichzeitig\ \ werden\ \ alle\ \ Normen\ \ von\ \ HplusminH\ \ be\
+rechnet\ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Do[\ {n = nlist[\([l]\)], \n\ \ \ \ \ \ \ Do[
+ Do[HtabplusminHtab[l, i, j] = \(HplusminH[i, j] =
+ SetPrecision[Htabplus[l, i, j] - Htab[l, i, j], gen]\), {i,
+ 1, n}, {j, 1, n}]], \n\t
+ NormDiffHil[l] = NormMat[HplusminH, n]}, {l, 1, 9}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ Ergebnis\ \ \ Differenzmatrix\ \ Hplus\ \
+ - \ H\ \ \ \ f\[UDoubleDot]r\ \ e\ i\ n\ e\ n\ \ Wert\ \ von\ \ nlist\ = \
+ lfest\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 3;\)\[IndentingNewLine]
+ Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\[IndentingNewLine]
+ TableForm[
+ Table[ScientificForm[
+ PaddedForm[HtabplusminHtab[l, i, j]\ , {5, 3}]], {l, lfest,
+ lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox[\(Gau\[SZ] - Zerlegung\ der\ Matrix\ A\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["=",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["H",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[\((\ ohne\ Zeilenvertauschung\ )\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], "\[IndentingNewLine]", " ",
+
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ Dreiecks - Zerlegung\ der\ Matrix\ A\ \ = \
+ H\ \((\ erste\ k - Schleife\ )\)\ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]], "\n",
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]],
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+
+ StyleBox[\(Vorw\[ADoubleDot]rtsrechnung\ \((\
+ erste\ i - Schleife\ \ \ )\)\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[",",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None]}]],
+
+ StyleBox[\(R\[UDoubleDot]ckw\[ADoubleDot]rtsrechnung\ \((\
+ zweite\ i - Schleife\ )\)\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{n = nlist[\([l]\)], \n\ \ \ \ \ \ \tDo[
+ Do[\ A[i, j] = H[i, j], {i, 1, n}], {j, 1, n}], \n\t\t\t\tDo[
+ Do[{A[i, k] = A[i, k]/A[k, k],
+ Do[A[i, j] = A[i, j] - A[i, k]*A[k, j], {j, k + 1, n}]}, {i,
+ k + 1, n}], {k, 1,
+ n - 1}], \n\t\t\t\tDo[{Do[{b[i] =
+ If[i == k, SetPrecision[1, gen], 0],
+ sumAb = SetPrecision[0. , gen], \n\t\t\t\tDo[
+ sumAb = sumAb + A[i, j]*b[j], {j, 1, i - 1}],
+ b[i] = b[i] - sumAb}, {i, 1,
+ n}], \n\t\t\t\t\t\tDo[{sumAX = SetPrecision[0. , gen],
+ Do[sumAX = sumAX + A[i, j]*Xgauss[l, j, k], {j, i + 1,
+ n}], \n\t\t\t\t\t\t\ \ \ \ \ \ Xgauss[l, i,
+ k] = \((b[i] - sumAX)\)/A[i, i]}, {i, n,
+ 1, \(-1\)}]}, {k, 1,
+ n}], \[IndentingNewLine]\ \ \ \ \ \ \ \ If[
+ Abs[A[n, n]] \[LessEqual] \
+ 10^\((\(-st\) +
+ 2)\), \[IndentingNewLine]\ \ \ \ \ \ Print["\<Achtung: die \
+Matrix ist bei der Ordnung n = \>",
+ n, "\< fast singul\[ADoubleDot]r !!! \>"\ , \[IndentingNewLine]\ \
+\ \ \ "\< A(n,n) = \>", \ PaddedForm[A[n, n], {6, 3}]]\ ]\ }, \t\n\t{l, 1,
+ 9}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox[\(Ausgabe\ \ der\ \ Gau\[SZ]\ - \
+ Zerlegung\ \ von\ \ A\ , \ \ zu\ \ Testzwecken\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]}]], "Input",
+ FontColor->RGBColor[0, 1, 0],
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ StyleBox[\(\(\ \ \)\(\(lfest = 1;\)\(\[IndentingNewLine]\)\(\n\)
+ \(\ \ \)\(TableForm[
+ Table[\ ScientificForm[PaddedForm[A[i, j], {st, st - 1}]], {i, 1,
+ nlist[\([lfest]\)]}, \n\t\t\t\ \ {j, 1, nlist[\([lfest]\)]}], \
+ TableSpacing -> {2, 1}]\)\(\ \ \)\)\),
+ FontColor->RGBColor[1, 0, 1]]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ \
+Ergebnis\ \ Xgauss\ \ ist\ \ die\ \ nach\ \ Gau\[SZ]\
+\ \ berechnete\ \ inverse\ \ Hilbertmatrix\ H^\(-1\)\ \n\t\t\t\ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ f\[UDoubleDot]r\ \ e\ i\ n\ e\ n\ \
+Wert\ \ von\ \ nlist\ = \ lfest\ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], " "}]],
+ "Subsubtitle"], " "}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 4;\)\[IndentingNewLine]
+ Print["\<Die Ordnung der Matrix ist: n = \>", nlist[\([lfest]\)]]\n
+ TableForm[
+ Table[ScientificForm[PaddedForm[Xgauss[l, i, j]\ , {st, st - 1}]], {l,
+ lfest, lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox[\(Cholesky - Zerlegung\ der\ Matrix\ A\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["=",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["H",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[\((\ verketteter\ Algorithmus\ )\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], "\[IndentingNewLine]",
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ " "}]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ Cholesky\ - \
+ Zerlegung\ \ der\ \ Matrix\ \ A\ \ = \ \ H\ \ \ \((\
+ erste\ k - Schleife\ )\)\ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]], "\n",
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]],
+ RowBox[{
+
+ StyleBox[\(Vorw\[ADoubleDot]rtsrechnung\ \((\
+ erste\ i - Schleife\ \ \ )\)\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[",",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None]}]],
+
+ StyleBox[\(R\[UDoubleDot]ckw\[ADoubleDot]rtsrechnung\ \((\
+ zweite\ i - Schleife\ )\)\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->None]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{"Do", "[",
+ RowBox[{
+ RowBox[{"{",
+
+ RowBox[{\(n = nlist[\([l]\)]\), ",", "\n",
+ " \t", \(Do[Do[\ A[i, j] = H[i, j], {i, 1, n}], {j, 1, n}]\),
+ ",", "\n",
+ "\t\t", \(Do[{Do[{sumAjiAjk = SetPrecision[0. , gen],
+ Do[sumAjiAjk = sumAjiAjk + A[j, i]*A[j, k], {j, 1,
+ i - 1}], \n\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \tA[i,
+ k] = \((A[i, k] - sumAjiAjk)\)/A[i, i]}, {i, 1,
+ k - 1}],
+ sumAjk2 =
+ SetPrecision[0. ,
+ gen], \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Do[
+ sumAjk2 = sumAjk2 + A[j, k]*A[j, k], {j, 1,
+ k - 1}], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+AkkminsumAjk2 = SetPrecision[A[k, k] - sumAjk2, gen],
+ A[k, k] =
+ SetPrecision[Sqrt[AkkminsumAjk2],
+ gen]}, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+{k, 1, n}]\), ",", "\t\t", "\n",
+ "\t\t", \(Do[{Do[{b[i] = If[i == k, SetPrecision[1, gen], 0],
+ sumAb = SetPrecision[0. , gen], \n\t\t\ \ \ \ \ Do[
+ sumAb = sumAb + A[j, i]*b[j], {j, 1, i - 1}],
+ b[i] = \((b[i] - sumAb)\)/A[i, i]}, {i, 1,
+ n}], \n\t\ \ \ \ \ \tDo[{sumAX = SetPrecision[0. , gen],
+ Do[sumAX = sumAX + A[i, j]*Xchol[l, j, k], {j, i + 1,
+ n}], \n\t\t\tXchol[l, i, k] = \((b[i] - sumAX)\)/
+ A[i, i]}, {i, n,
+ 1, \(-1\)}]\ \ \ }, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \
+\ \ \ \ {k, 1, n}]\), " ", ",", " ",
+
+ StyleBox[\( (*\ \ \(Print[\ "\<l= \>", l, "\< \>",
+ AkkminsumAjk2, "\< \>", A[n, n]]\)\(,\)\ \ *) \),
+ Background->RGBColor[1, 1, 0]], "\[IndentingNewLine]",
+ " ", \(If[AkkminsumAjk2 \[LessEqual] 10. ^\((\(-st\) + 2)\),
+ Print["\< Die Matrix ist bei der Ordnung n = \>",
+ n, "\< nicht mehr positiv definit !!! \>"\ , \ "\< A(n,n) = \
+\>", PaddedForm[A[n, n], {4, 3}]]]\)}], " ", "}"}], ",", "\n",
+ " ", \({l, 1, 9}\)}], "]"}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]], " "}]],
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[\(Ausgabe\ \ der\ \ Cholesky - \
+ Zerlegung\ \ von\ \ A\ \ , \ \ \ zu\ \ \ \ Testzwecken\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]}]], "Input",
+ FontColor->RGBColor[0, 1, 0],
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[{
+ StyleBox[\(\(\ \)\(lfest = 1;\)\),
+ FontColor->RGBColor[1, 0, 1]], "\n",
+ StyleBox[\(\(\ \)\(TableForm[
+ Table[\ ScientificForm[PaddedForm[A[i, j], {st, st - 1}]], {i, 1,
+ nlist[\([lfest]\)]}, \n\t\t\t\ \ {j, 1, nlist[\([lfest]\)]}], \
+ TableSpacing -> {2, 1}]\)\(\ \ \)\),
+ FontColor->RGBColor[1, 0, 1]]}], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ Ergebnis\ \ Xchol\ \ ist\ die\ nach\ Cholesky\ \
+berechnete\ \ inverse\ \ Hilbertmatrix\ H^\(-1\)\ \n\t\t\t\ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ f\[UDoubleDot]r\ \ e\ i\ n\ e\ n\ Wert\ \ von\ nlist\ \
+= \ lfest\ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], " "}]],
+ "Subsubtitle"], " "}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 4;\)\n
+ Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\[IndentingNewLine]
+ TableForm[
+ Table[Chop[
+ ScientificForm[PaddedForm[Xchol[l, i, j]\ , {st, st - 1}]]], {l,
+ lfest, lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+
+ StyleBox[\(\
+Erstellen\ \ der\ \ exakten\ \ inversen\ \ Hilbertmatrix\ \ Xexakt\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["=",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox[\(H^\(-1\)\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], "\[IndentingNewLine]", " ",
+
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\t\)\(Do[{n = nlist[\([l]\)], \n\ \ \ \ \ \ \ \ \ \ \ \ \ Do[
+ Do[Xexakttab[l, i, j] = \ \(Xexakt[i, j] =
+ SetPrecision[Fakul[n + i - 1],
+ gen]*\((\(-1\))\)^\((i +
+ j)\)/\n\t\ \ \ \ \ \ \ \((\((i + j - 1)\)*
+ SetPrecision[\ Fakul[i - 1]^2, gen]*
+ SetPrecision[Fakul[j - 1]^2, gen]*
+ SetPrecision[Fakul[n - i], gen]*
+ SetPrecision[Fakul[n - j], gen])\)*
+ SetPrecision[Fakul[n + j - 1],
+ gen]\), \[IndentingNewLine]\t{i, 1, n}], {j, \ 1,
+ n}]\ , \ NormHilInv[l] =
+ NormMat[Xexakt, n]}, \[IndentingNewLine]\t\ \ {\ l, 1,
+ 9}\ ]\)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ \ \ \ \ \
+Ergebnis\ \ Xexakt\ \ ist\ \ die\ \ exakte\ \ inverse\ \ Hilbertmatrix\ \
+H^\(-1\)\ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f\[UDoubleDot]r\ \ e\ i\ n\ e\ \
+n\ \ Wert\ \ von\ \ nlist\ = \ lfest\ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 4;\)\t\n
+ Print["\<Die Ordnung der Matrix ist: n = \>",
+ nlist[\([lfest]\)]]\[IndentingNewLine]
+ TableForm[
+ Table[ScientificForm[
+ PaddedForm[Xexakttab[l, i, j]\ , {st, st - 1}]], {l, lfest,
+ lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]],
+ RowBox[{
+ StyleBox[\(Erstellen\ \ der\ \ Differenzmatrix\ \ Xexakt\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["-",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["Xgauss",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\(\(\ \ \ \)\(\ \)\(\ \ \)\)
+ Gleichzeitig\ \ werden\ \ alle\ \ Normen\ \ von\ \ XexaminXgau\ \ b\
+erechnet\ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{n = nlist[\([l]\)], \n
+ Do[Do[XexaminXgautab[l, i, j] = \(XexaminXgau[i, j] =
+ Xexakttab[l, i, j] - Xgauss[l, i, j]\), {i, 1, n}], {j, 1,
+ n}], \n\tNormDiffHilInv[l] = NormMat[XexaminXgau, n]}, {l, 1,
+ 9}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ \ \ \ Ergebnis\ \ \ Diferenzmatrix\ \ Xexakt\ - \
+ Xgauss\ \ \ \ f\[UDoubleDot]r\ \ e\ i\ n\ e\ \
+n\ \ Wert\ \ von\ \ nlist\ = lfest\ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 3;\)\t\n
+ TableForm[
+ Table[ScientificForm[
+ PaddedForm[
+ XexaminXgautab[l, i, j], {st,
+ st - 1}]], \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \t\t\
+{l, lfest, lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]],
+ RowBox[{
+ StyleBox[\(Erstellen\ \ der\ \ Differenzmatrix\ \ Xchol\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["-",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["Xgauss",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\(\(\ \ \ \)\(\ \)\(\ \ \)\)
+ Gleichzeitig\ \ werden\ \ alle\ \ Normen\ \ von\ \ XcholminXgau\ \ b\
+erechnet\ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{n = nlist[\([l]\)], \n
+ Do[Do[XcholminXgautab[l, i, j] = \(XcholminXgau[i, j] =
+ Xchol[l, i, j] - Xgauss[l, i, j]\), {i, 1, n}], {j, 1,
+ n}], \n\tNormDiffCholGau[l] = NormMat[XcholminXgau, n]}, {l, 1,
+ 9}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["(*",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]],
+ RowBox[{
+ StyleBox[\(Erstellen\ \ der\ \ Differenzmatrix\ \ Xexakt\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["-",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ RowBox[{
+ StyleBox["Xchol",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["alle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Werte",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["von",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["*)",
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\(\(\ \ \ \)\(\ \)\(\ \ \)\)
+ Gleichzeitig\ \ werden\ \ alle\ \ Normen\ \ von\ \ XexaminXchol\ \ b\
+erechnet\ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{n = nlist[\([l]\)], \n
+ Do[Do[XexaminXcholtab[l, i, j] = \(XexaminXchol[i, j] =
+ Xexakttab[l, i, j] - Xchol[l, i, j]\), {i, 1, n}], {j, 1,
+ n}], \n\tNormDiffHilInvChol[l] = NormMat[XexaminXchol, n]}, {l,
+ 1, 9}]\)], "Input"],
+
+Cell[BoxData[
+ \(TableForm[
+ Do[Print[ScientificForm[
+ PaddedForm[NormDiffHilInv[l], {15, 6}]], "\< \>",
+ ScientificForm[
+ PaddedForm[NormDiffHilInvChol[l], {15, 6}]], "\< \>",
+ ScientificForm[PaddedForm[NormDiffCholGau[l], {15, 6}]]], {l, 1,
+ 9}]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ \ \ \ Ergebnis\ \ \ Differenzmatrix\ \ Xexakt\ - \
+ Xchol\ \ \ \ f\[UDoubleDot]r\ \ e\ i\ n\ e\ \
+n\ \ Wert\ \ von\ \ nlist\ = lfest\ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\(lfest = 3;\)\t\n
+ TableForm[
+ Table[ScientificForm[
+ PaddedForm[
+ XexaminXcholtab[l, i, j], {st,
+ st - 1}]], \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \t\t\
+{l, lfest, lfest}, {i, 1, nlist[\([l]\)]}, {j, 1, nlist[\([l]\)]}],
+ TableSpacing -> {2, 1}]\)\(\ \ \)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[\(Erstellen\ \ des\ \ Tabellenkopfes\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle"], " "}]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(Tabelle[0, 1] = "\< n\>"; Tabelle[0, 2] = "\< || Hil || \>";
+ Tabelle[0, 3] = "\<|| HilInV||\>"; Tabelle[0, 4] = "\<||Hplus-Hil||\>";\n
+ Tabelle[0, 5] = "\<||Exakt-Xgau\[SZ]|| \>";
+ Tabelle[0, 6] = "\< Kond_Fakt\>";
+ Tabelle[0, 7] = "\< Cond_Zahl\>";\)\(\t\)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ RowBox[{
+ RowBox[{
+ StyleBox["Erstellen",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["der",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Tabelle",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["mit",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle"]}]],
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Berechnung",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["des",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["Konditionsfaktors",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["k",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["und",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", " ",
+ StyleBox["der",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Konditionszahl",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["\[Mu]",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["=",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[\(cond \((H)\)\),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]],
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{Tabelle[i, 1] = nlist[\([i]\)], \ Tabelle[i, 2] = NormHil[i], \
+ Tabelle[i, 3] = NormHilInv[i], \ Tabelle[i, 4] = NormDiffHil[i],
+ Tabelle[i, 5] = NormDiffHilInv[i],
+ Tabelle[i, 6] = \(kfakt[i] =
+ NormHil[i]/NormHilInv[i]*
+ NormDiffHilInv[i]/NormDiffHil[i]\)\ , \n\ \ \ \ \ Tabelle[i,
+ 7] = \(mue[i] = NormHil[i]*NormHilInv[i]\)}, \ \ {i, 1,
+ 9}\ ]\)], "Input"],
+
+Cell[BoxData[
+ \(\(genlist = {3, {6, 3}, {4, 3}, {4, 3}, {5, 3}, {4, 3}, {4,
+ 3}};\)\)], "Input"],
+
+Cell[BoxData[
+ \(TableForm[
+ Table[ScientificForm[PaddedForm[Tabelle[i, j], genlist[\([j]\)]]], {i,
+ 0, 9}, {j, 1, 7}], TableSpacing -> {2, 1}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[\( (*\ \ \ \ \ \ \ Graphische\ \ Darstellung\ \ der\ \
+Konditionszahlen\ \ \[Mu]\ \ und\ Konditionsfaktoren\ \ k\ \ \ \ *) \),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]], " "}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(<< Graphics`Colors`\)], "Input"],
+
+Cell[BoxData[
+ \(\(farblist\ = \ {\ Cyan, Green, \ Brown, \ Blue,
+ Magenta\ };\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Subsubtitle"]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Konditionsfaktoren\ \ \ k\
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[{\(Print["\< Konditionsfaktoren k \
+\>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabpkte[ipl]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1], Log[10. , Tabelle[n, 6]]}, {n, 1, 9}],
+ PlotJoined\ -> \ False, \n\tPlotRange -> {{0, 20}, {0, 30}},
+ Prolog\ -> \ AbsolutePointSize[4],
+ PlotStyle \[Rule] farblist[\([ipl]\)], AspectRatio -> 0.6,
+ PlotLabel \[Rule] "\<\>",
+ AxesLabel -> {"\<> n\>", "\< ^ lg(k)\>"}\), "]"}]}]}], "Input"],
+
+Cell[BoxData[{\(Print["\< Konditionsfaktoren k\>"];\), \
+"\[IndentingNewLine]",
+ RowBox[{\(Tabsp[ipl]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1], Log[10. , Tabelle[n, 6]]}, {n, 1, 9}],
+ PlotJoined\ -> \ True, \n\ \ \ \ PlotRange -> {{0, 20}, {0, 30}},
+ PlotStyle \[Rule] farblist[\([ipl]\)], AspectRatio -> 0.6,
+ PlotLabel \[Rule] "\<\>",
+ AxesLabel -> {"\<> n\>", "\< ^ lg(k)\>"}\), "]"}]}]}], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ "Subsubtitle"]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Konditionszahlen\
+\ \ \ \ \ \[Mu]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(Tabelle[0, 1]\ = \ 1; \ Tabelle[0, 7] = 1. ;\)], "Input"],
+
+Cell[BoxData[{\(Print["\< Konditionszahlen \
+\[Mu]\>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabpkte[0]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1], Log[10. , Tabelle[n, 7]]}, {n, 0, 9}],
+ PlotJoined\ -> \ False, \n\tPlotRange -> {{0, 20}, {0, 30}},
+ Prolog\ -> \ AbsolutePointSize[4], PlotStyle \[Rule] Red,
+ AspectRatio -> 0.6, PlotLabel \[Rule] "\<\>",
+ AxesLabel -> {"\<> n\>", "\< ^ lg(\[Mu])\>"}\), "]"}]}]}], "Input"],
+
+Cell[BoxData[{\(Print["\< Konditionszahlenen \
+\[Mu]\>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabsp[0]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1], Log[10. , Tabelle[n, 7]]}, {n, 0, 9}],
+ PlotJoined\ -> \ True, \n\tPlotRange -> {{0, 20}, {0, 30}},
+ PlotStyle \[Rule] Red, AspectRatio -> 0.6, PlotLabel \[Rule] "\<\>",
+ AxesLabel -> {"\<> n\>", "\< ^ lg(\[Mu])\>"}\),
+ "]"}]}]}], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[\(Nummern \(\(\ \)\(\ \)\)
+ der\ \ auszugebenden\ Kurven\ festlegen\),
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[{
+ \(\(If\ [\
+ ipl\ == \ 1, \ {\ ipl1\ = \ 1; \
+ ipl2\ = \ 1; \ \ ipl3\ = \ 1; \ \ ipl4\ = \ 1,
+ ipl5\ = \ 1\ }];\)\), "\[IndentingNewLine]",
+ \(\(If\ [\
+ ipl\ == \ 2, \ {\ ipl1\ = \ 1; \
+ ipl2\ = \ 2; \ \ ipl3\ = \ 1; \ \ ipl4\ = \ 1,
+ ipl5\ = \ 1\ }];\)\), "\[IndentingNewLine]",
+ \(\(If\ [\
+ ipl\ == \ 3, \ {\ ipl1\ = \ 1; \
+ ipl2\ = \ 2; \ \ ipl3\ = \ 3; \ \ ipl4\ = \ 1,
+ ipl5\ = \ 1\ }];\)\), "\[IndentingNewLine]",
+ \(\(If\ [\
+ ipl\ == \ 4, \ {\ ipl1\ = \ 1; \
+ ipl2\ = \ 2; \ \ ipl3\ = \ 3; \ \ ipl4\ = \ 4,
+ ipl5\ = \ 1\ }];\)\), "\[IndentingNewLine]",
+ \(\(If\ [\
+ ipl\ == \ 5, \ {\ ipl1\ = \ 1; \
+ ipl2\ = \ 2; \ \ ipl3\ = \ 3; \ \ ipl4\ = \ 4,
+ ipl5\ = \ 5\ }];\)\)}], "Input"],
+
+Cell[BoxData[
+ StyleBox[\( (*\ \ \ Gesamtgraphik : \ \ \
+Konditionszahlen\ \ und\ \ Konditionsfaktoren\ f\[UDoubleDot]r\ \ st\ = \ \ \
+8\ , \ 12, \ 16\ , \ 20\ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[{
+ \(\(Print["\< Konditionsfaktoren und \
+Konditionszahlen\>"];\)\), "\[IndentingNewLine]",
+ \(Show[Tabsp[0], Tabsp[ipl1], Tabsp[ipl2], Tabsp[ipl3], Tabsp[ipl4],
+ Tabsp[ipl5], Tabpkte[0], Tabpkte[ipl1], Tabpkte[ipl2], Tabpkte[ipl3],
+ Tabpkte[ipl4], Tabpkte[ipl5],
+ Prolog\ -> \ AbsolutePointSize[4]]\)}], "Input"],
+
+Cell[BoxData[
+ StyleBox[
+ RowBox[{"(*", " ",
+ RowBox[{
+ "Relativer", " ", "Fehler", " ", "bei", " ", "der", " ", "Berechnung",
+ " ", "der", " ", "inversen", " ", "Matrizen", " ",
+ StyleBox[
+ RowBox[{"f",
+ StyleBox["\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], " ", "alle", " ", "Werte",
+ " ", "von", " ", "nlist"}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], " "}]], "*)"}],
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[{\(Print["\< Relativer Fehler in % \
+\>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabpkteproz[ipl]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1],
+ 100*NormDiffHilInv[n]/NormHilInv[n]}, {n, 1, 9}],
+ PlotJoined\ -> \ False, \n\tPlotRange -> {{0, 20}, {\(-10\), 150}},
+ Prolog\ -> \ AbsolutePointSize[4],
+ PlotStyle \[Rule] farblist[\([ipl]\)], AspectRatio -> 0.6,
+ PlotLabel \[Rule] "\<\>", AxesLabel -> {"\<> n\>", "\< ^ %\>"}\),
+ "]"}]}]}], "Input"],
+
+Cell[BoxData[{\(Print["\< Relativer Fehler in % \
+\>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabspproz[ipl]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1],
+ 100*NormDiffHilInv[n]/NormHilInv[n]}, {n, 1, 9}],
+ PlotJoined\ -> \ True, \n\tPlotRange -> {{0, 20}, {\(-10\), 150}},
+ Prolog\ -> \ AbsolutePointSize[4],
+ PlotStyle \[Rule] farblist[\([ipl]\)], AspectRatio -> 0.6,
+ PlotLabel \[Rule] "\<\>", AxesLabel -> {"\<> n\>", "\< ^ %\>"}\),
+ "]"}]}]}], "Input"],
+
+Cell[BoxData[{
+ \(\(Print["\< Relativer Fehler in % \>"];\)\), "\
+\[IndentingNewLine]",
+ \(Show[Tabspproz[ipl1], Tabspproz[ipl2], Tabspproz[ipl3],
+ Tabspproz[ipl4], Tabspproz[ipl5], Tabpkteproz[ipl1], Tabpkteproz[ipl2],
+ Tabpkteproz[ipl3], Tabpkteproz[ipl4], Tabpkteproz[ipl5],
+ Prolog\ -> \ AbsolutePointSize[4]]\)}], "Input"],
+
+Cell[BoxData[
+ StyleBox[
+ RowBox[{"(*", " ",
+ RowBox[{
+ "Relativer", " ", "Fehler", " ", "bei", " ", "der", " ", "Berechnung",
+ " ", "der", " ", "inversen", " ", "Matrizen", " ",
+ StyleBox[
+ RowBox[{"f",
+ StyleBox["\[UDoubleDot]r",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], " ", "alle", " ", "Werte",
+ " ", "von", " ", "nlist"}],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], " "}]], "*)"}],
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[{\(Print["\< Relativer Fehler in Log % \
+\>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabpktelog[ipl]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1],
+ Log[10, 100*NormDiffHilInv[n]/NormHilInv[n]]}, {n, 1, 9}],
+ PlotJoined\ -> \ False, \n\tPlotRange -> {{0, 20}, {\(-21\), 5}},
+ Prolog\ -> \ AbsolutePointSize[4],
+ PlotStyle \[Rule] farblist[\([ipl]\)], AspectRatio -> 0.6,
+ PlotLabel \[Rule] "\<\>",
+ AxesLabel -> {"\<> n\>", "\< ^ Log %\>"}\), "]"}]}]}], "Input"],
+
+Cell[BoxData[{\(Print["\< Relativer Fehler in Log % \
+\>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabsplog[ipl]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1],
+ Log[10, 100*NormDiffHilInv[n]/NormHilInv[n]]}, {n, 1, 9}],
+ PlotJoined\ -> \ True, \n\tPlotRange -> {{0, 20}, {\(-21\), 5}},
+ Prolog\ -> \ AbsolutePointSize[4],
+ PlotStyle \[Rule] farblist[\([ipl]\)], AspectRatio -> 0.6,
+ PlotLabel \[Rule] "\<\>",
+ AxesLabel -> {"\<> n\>", "\< ^ Log %\>"}\), "]"}]}]}], "Input"],
+
+Cell[BoxData[{
+ \(\(Print["\< Relativer Fehler in % \>"];\)\
+\), "\[IndentingNewLine]",
+ \(Show[Tabsplog[ipl1], Tabsplog[ipl2], Tabsplog[ipl3], Tabsplog[ipl4],
+ Tabsplog[ipl5], Tabpktelog[ipl1], Tabpktelog[ipl2], Tabpktelog[ipl3],
+ Tabpktelog[ipl4], Tabpktelog[ipl5],
+ Prolog\ -> \ AbsolutePointSize[4]]\)}], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ RowBox[{
+ StyleBox["Unterschied",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["zwischen",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Gauss",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["und",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Cholesky",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["beim",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Invertieren",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["f\[UDoubleDot]r",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["alle",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["Werte",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["von",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[" ",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["nlist",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ "Section",
+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]], " "}]],
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["*)",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[{\(Print["\< Unterschied D = Gauss - \
+Cholesky \>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabpktediff[ipl]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1], Log[10, NormDiffCholGau[n]]}, {n, 1,
+ 9}], PlotJoined\ -> \ False, \n\t
+ PlotRange -> {{0, 20}, {\(-35\), 20}},
+ Prolog\ -> \ AbsolutePointSize[4],
+ PlotStyle \[Rule] farblist[\([ipl]\)], AspectRatio -> 0.6,
+ PlotLabel \[Rule] "\<\>",
+ AxesLabel -> {"\<> n\>", "\< ^ lg(D)\>"}\), "]"}]}]}], "Input"],
+
+Cell[BoxData[{\(Print["\< Unterschied D = Gauss - \
+Cholesky \>"];\), "\[IndentingNewLine]",
+ RowBox[{\(Tabspdiff[ipl]\), "=",
+ RowBox[{
+ StyleBox["ListPlot",
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]],
+ "[", \(Table[{Tabelle[n, 1], Log[10, NormDiffCholGau[n]]}, {n, 1,
+ 9}], PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{0, 20}, {\(-35\), 20}},
+ Prolog\ -> \ AbsolutePointSize[4],
+ PlotStyle \[Rule] farblist[\([ipl]\)], AspectRatio -> 0.6,
+ PlotLabel \[Rule] "\<\>",
+ AxesLabel -> {"\<> n\>", "\< ^ lg(D)\>"}\), "]"}]}]}], "Input"],
+
+Cell[BoxData[
+ \(Show[Tabpktediff[ipl1], Tabpktediff[ipl2], Tabpktediff[ipl3],
+ Tabpktediff[ipl4], Tabpktediff[ipl5], Tabspdiff[ipl1], Tabspdiff[ipl2],
+ Tabspdiff[ipl3], Tabspdiff[ipl4], Tabspdiff[ipl5]]\)], "Input"],
+
+Cell[BoxData[""], "Input"]
+},
+FrontEndVersion->"5.0 for Microsoft Windows",
+ScreenRectangle->{{0, 1024}, {0, 685}},
+WindowSize->{1016, 651},
+WindowMargins->{{0, Automatic}, {Automatic, 0}},
+PrintingCopies->1,
+PrintingPageRange->{Automatic, Automatic},
+Magnification->1
+]
+
+(*******************************************************************
+Cached data follows. If you edit this Notebook file directly, not
+using Mathematica, you must remove the line containing CacheID at
+the top of the file. The cache data will then be recreated when
+you save this file from within Mathematica.
+*******************************************************************)
+
+(*CellTagsOutline
+CellTagsIndex->{}
+*)
+
+(*CellTagsIndex
+CellTagsIndex->{}
+*)
+
+(*NotebookFileOutline
+Notebook[{
+Cell[1754, 51, 290, 6, 59, "Input"],
+Cell[2047, 59, 52, 1, 30, "Input"],
+Cell[2102, 62, 2929, 91, 46, "Input"],
+Cell[5034, 155, 876, 20, 70, "Input"],
+Cell[5913, 177, 253, 5, 54, "Input"],
+Cell[6169, 184, 165, 3, 46, "Input"],
+Cell[6337, 189, 113, 2, 30, "Input"],
+Cell[6453, 193, 281, 6, 49, "Input"],
+Cell[6737, 201, 85, 1, 30, "Input"],
+Cell[6825, 204, 604, 19, 46, "Input"],
+Cell[7432, 225, 593, 12, 72, "Input"],
+Cell[8028, 239, 71, 1, 30, "Input"],
+Cell[8102, 242, 245, 5, 49, "Input"],
+Cell[8350, 249, 300, 6, 99, "Input"],
+Cell[8653, 257, 257, 6, 49, "Input"],
+Cell[8913, 265, 88, 1, 30, "Input"],
+Cell[9004, 268, 3359, 103, 49, "Input"],
+Cell[12366, 373, 254, 5, 70, "Input"],
+Cell[12623, 380, 5397, 155, 66, "Input"],
+Cell[18023, 537, 389, 8, 90, "Input"],
+Cell[18415, 547, 164, 3, 30, "Input"],
+Cell[18582, 552, 170, 3, 50, "Input"],
+Cell[18755, 557, 73, 1, 30, "Input"],
+Cell[18831, 560, 377, 8, 90, "Input"],
+Cell[19211, 570, 3700, 112, 69, "Input"],
+Cell[22914, 684, 288, 5, 70, "Input"],
+Cell[23205, 691, 420, 8, 73, "Input"],
+Cell[23628, 701, 394, 7, 90, "Input"],
+Cell[24025, 710, 156, 3, 30, "Input"],
+Cell[24184, 715, 172, 3, 50, "Input"],
+Cell[24359, 720, 65, 1, 30, "Input"],
+Cell[24427, 723, 337, 6, 70, "Input"],
+Cell[24767, 731, 3031, 89, 69, "Input"],
+Cell[27801, 822, 315, 5, 70, "Input"],
+Cell[28119, 829, 700, 18, 46, "Input"],
+Cell[28822, 849, 388, 8, 90, "Input"],
+Cell[29213, 859, 3549, 100, 71, "Input"],
+Cell[32765, 961, 2344, 71, 66, "Input"],
+Cell[35112, 1034, 1293, 23, 230, "Input"],
+Cell[36408, 1059, 876, 27, 46, "Input"],
+Cell[37287, 1088, 355, 6, 90, "Input"],
+Cell[37645, 1096, 709, 18, 66, "Input"],
+Cell[38357, 1116, 350, 6, 90, "Input"],
+Cell[38710, 1124, 3760, 106, 71, "Input"],
+Cell[42473, 1232, 2408, 72, 66, "Input"],
+Cell[44884, 1306, 2313, 41, 310, "Input"],
+Cell[47200, 1349, 767, 23, 46, "Input"],
+Cell[47970, 1374, 376, 7, 70, "Input"],
+Cell[48349, 1383, 702, 17, 66, "Input"],
+Cell[49054, 1402, 373, 8, 90, "Input"],
+Cell[49430, 1412, 2929, 87, 71, "Input"],
+Cell[52362, 1501, 795, 14, 130, "Input"],
+Cell[53160, 1517, 872, 21, 66, "Input"],
+Cell[54035, 1540, 375, 8, 90, "Input"],
+Cell[54413, 1550, 3248, 96, 69, "Input"],
+Cell[57664, 1648, 285, 5, 70, "Input"],
+Cell[57952, 1655, 661, 18, 46, "Input"],
+Cell[58616, 1675, 351, 8, 70, "Input"],
+Cell[58970, 1685, 3248, 96, 69, "Input"],
+Cell[62221, 1783, 285, 5, 70, "Input"],
+Cell[62509, 1790, 3248, 96, 69, "Input"],
+Cell[65760, 1888, 291, 5, 70, "Input"],
+Cell[66054, 1895, 324, 7, 70, "Input"],
+Cell[66381, 1904, 661, 18, 46, "Input"],
+Cell[67045, 1924, 352, 8, 70, "Input"],
+Cell[67400, 1934, 937, 30, 46, "Input"],
+Cell[68340, 1966, 314, 5, 70, "Input"],
+Cell[68657, 1973, 4185, 125, 66, "Input"],
+Cell[72845, 2100, 454, 8, 70, "Input"],
+Cell[73302, 2110, 112, 2, 30, "Input"],
+Cell[73417, 2114, 174, 3, 30, "Input"],
+Cell[73594, 2119, 282, 6, 49, "Input"],
+Cell[73879, 2127, 52, 1, 30, "Input"],
+Cell[73934, 2130, 107, 2, 30, "Input"],
+Cell[74044, 2134, 387, 10, 46, "Input"],
+Cell[74434, 2146, 624, 12, 90, "Input"],
+Cell[75061, 2160, 581, 11, 90, "Input"],
+Cell[75645, 2173, 389, 10, 46, "Input"],
+Cell[76037, 2185, 78, 1, 30, "Input"],
+Cell[76118, 2188, 600, 11, 90, "Input"],
+Cell[76721, 2201, 565, 11, 70, "Input"],
+Cell[77289, 2214, 575, 18, 46, "Input"],
+Cell[77867, 2234, 891, 20, 110, "Input"],
+Cell[78761, 2256, 273, 6, 49, "Input"],
+Cell[79037, 2264, 366, 6, 70, "Input"],
+Cell[79406, 2272, 747, 20, 49, "Input"],
+Cell[80156, 2294, 652, 13, 90, "Input"],
+Cell[80811, 2309, 649, 13, 90, "Input"],
+Cell[81463, 2324, 366, 6, 70, "Input"],
+Cell[81832, 2332, 747, 20, 49, "Input"],
+Cell[82582, 2354, 670, 13, 90, "Input"],
+Cell[83255, 2369, 667, 13, 90, "Input"],
+Cell[83925, 2384, 373, 6, 70, "Input"],
+Cell[84301, 2392, 2749, 90, 46, "Input"],
+Cell[87053, 2484, 663, 13, 90, "Input"],
+Cell[87719, 2499, 660, 13, 90, "Input"],
+Cell[88382, 2514, 231, 3, 50, "Input"],
+Cell[88616, 2519, 26, 0, 30, "Input"]
+}
+]
+*)
+
+
+
+(*******************************************************************
+End of Mathematica Notebook file.
+*******************************************************************)
+
|