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| 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 | |
| download | Studium-33613a85afc4b1481367fbe92a17ee59c240250b.tar.gz Studium-33613a85afc4b1481367fbe92a17ee59c240250b.tar.bz2 | |
Diffstat (limited to 'Bachelor/Numerische Mathematik')
21 files changed, 61270 insertions, 0 deletions
diff --git a/Bachelor/Numerische Mathematik/Num05Aufg0.nb b/Bachelor/Numerische Mathematik/Num05Aufg0.nb new file mode 100644 index 0000000..2446849 --- /dev/null +++ b/Bachelor/Numerische Mathematik/Num05Aufg0.nb @@ -0,0 +1,699 @@ +(************** Content-type: application/mathematica **************
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+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ 0, .. , m\ \ eingeben\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
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+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(If[\
+ sch == "\<V\>", {\ \ m = 10, \[IndentingNewLine]\
+ xp[0] = \(-4. \); \ \ \ yp[0] =
+ 0. ; \ \ \ xp[1] = \(-3.95\); \ \ \ \ \ yp[1] =
+ 0.5; \ \ \ \ \ \ xp[2] = \(-3.5\); \ \ \ \ \ \ yp[2] =
+ 1.5; \ \ \ \ \ \ \ xp[3] = \(-3. \); \ \ \ yp[3] =
+ 2. ; \ \ \ xp[4] = \ \(-2\); \ \ \ \ \ \ \ \ \ \ yp[4] =
+ 2.6; \ \ \ \ \ \ xp[5] = \ \(-1\); \ \ \ \ \ \ \ \ \ yp[5] =
+ 2.9; \ \ \ \ \ \ \ \ \ xp[6] = \ \ \ 0. ; \ \ \ yp[6] =
+ 3. ; \ \ xp[7] = \ \ \ 2; \ \ \ \ \ \ \ \ \ \ \ yp[7] =
+ 2.6; \ \ \ \ \ \ \ xp[8] = \(+3. \); \ \ \ \ \ \ \ \ yp[8] =
+ 2. ; \n\ \ \ \ \ \ \ \ xp[9] = \ 3.75; \
+ yp[9] = 1; \ \ \ \ xp[10] = \(+4. \); \ \ \ \ \ \ yp[10] =
+ 0. ;\ \ \ }\ \ \ \ ];\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(Vorgegebene\ St\[UDoubleDot]tzpunkte\ 0, .. , m\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch == "\<V\>",
+ TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], "\< yp[\>", ind, "\<] = \>",
+ PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \
+L\[ODoubleDot]schen\ \ eines\ \ Punktes\ \ mit\ \ der\ \ Nummer\ \ index\ \ \ \
+*) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{\(index\ = \ 1\), " ", ";", " ",
+ StyleBox[\( (*\
+ Nummer\ des\ zu\ entfernenden\ Punktes\ \((\
+ index\ )\)\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]], " ", "\n",
+ " ", \(If[sch \[Equal] "\<L\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m\ , {m =
+ m - 1; \n\ \ \ \ \ \ \ \ \ Do[{\ xp[j] = xp[j + 1],
+ yp[j] = yp[j + 1]}, {j, index, m}]}]]\), ";",
+ " "}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Entfernen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<L\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m\ \ , \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \
+Einf\[UDoubleDot]gen\ \ eins\ \ Punktes\ \ mit\ \ der\ \ Nummer\ i\ ndex\ \ \ \
+\ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{\(index\ = \ 2\), " ", ";", " ",
+ StyleBox[\( (*\
+ Nummer\ des\ einzuf\[UDoubleDot]genden\ Punktes\ \((\
+ index\ )\)\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]], " ", "\[IndentingNewLine]",
+
+ RowBox[{"If", "[",
+ RowBox[{\(sch \[Equal] "\<E\>"\), ",",
+ RowBox[{"If", "[",
+
+ RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual] m\),
+ ",",
+ RowBox[{"{",
+
+ RowBox[{\(m = m + 1\),
+ ";", \(Do[{xp[j], yp[j]}, {j, 0, index - 1}]\), ";",
+ "\[IndentingNewLine]",
+ " ", \(Do[{xp[j] = xp[j - 1], yp[j] = yp[j - 1]}, {j,
+ m, index + 1, \(-1\)}]\), ";", "\[IndentingNewLine]",
+ " ", \(xp[index] = \ \ 3.75\),
+ " ",
+ StyleBox[\( (*\ xp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]",
+ " ", \(yp[index] = \ \ \ 1.0\)}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox[\( (*\ yp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["}",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]]}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<E\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m, \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \[CapitalADoubleDot]ndern\ des\ Punktes\ mit\ \
+der\ Nummer\ index\ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{\(index\ = \ \ 2\), ";", " ",
+ StyleBox[\( (*\
+ Nummer\ des\ zu\ \[ADoubleDot]ndernden\ Punktes\ \((\
+ index\ )\)\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]], " ", "\n", " ",
+ RowBox[{"If", "[",
+ RowBox[{\(sch \[Equal] "\<K\>"\), ",",
+ RowBox[{"If", "[",
+
+ RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual] m\),
+ ",",
+ RowBox[{"{", " ",
+
+ RowBox[{\(xp[index] = \ \ \ \(-3.75\)\),
+ " ",
+ StyleBox[\( (*\ xp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]",
+ " ", \(yp[index] = \ \ \ 1.0\)}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox[\( (*\ yp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["}",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]]}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<K\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m, \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ \(\(nummer[lauf] = m;\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ St\[UDoubleDot]tzstellen\ f\[UDoubleDot]r\
+\ den\ Graph\ der\ Ellipse\ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(nd = 400;\)\)], "Input"],
+
+Cell[BoxData[
+ \(Do[{xel[j] = xp[0] + j*\((xp[m] - xp[0])\)/nd,
+ yel[j] = 3/4*Sqrt[16 - xel[j]^2]}, {j, 0, nd}]\)], "Input"],
+
+Cell[BoxData[
+ \(<< Graphics`Colors`\)], "Input"],
+
+Cell[BoxData[
+ \(\(liste1 = {Red, HotPink, Green, Apricot, Brown, DarkGreen, Cobalt,
+ Brick, Orange, Magenta, IndianRed, ForestGreen};\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ Plotten\ der\ Ellipse\ \ x\^2\/16\
+\ + \ y\^2\/9 = \ 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(ellipsplot =
+ ListPlot[Table[{xel[j], yel[j]}, {j, 0, nd}],
+ PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{\(-5\), 5}, {\(-1\), 4}}, \tPlotStyle -> Brown,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(linienplot =
+ ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ True, \t
+ PlotRange -> {{\(-5\), 5}, {\(-1\), 4}}, \n\tPlotStyle -> Blue,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(punktplot =
+ ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ False, \t
+ PlotRange -> {{\(-5\), 5}, {\(-1\), 4}}, \n\tPlotStyle -> Blue,
+ Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5,
+ AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(Show[ellipsplot, linienplot, punktplot,
+ Prolog\ -> \ AbsolutePointSize[5]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Newton\ - \
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ *) \),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ Dividierte\ Differenzen\ f\
+\[UDoubleDot]r\ die\ Newton - Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(Do[DivDiff[k, 1] = \((yp[k + 1] - yp[k])\)/\((xp[k + 1] - xp[k])\), {k,
+ 0, m - 1}]\)], "Input"],
+
+Cell[BoxData[
+ \(Do[Do[
+ DivDiff[k,
+ j] = \((DivDiff[k + 1, j - 1] -
+ DivDiff[k, j - 1])\)/\((xp[k + j] - xp[k])\), {k, 0,
+ m - j}], {j, 2, m}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ St\[UDoubleDot]tzstellen\ f\[UDoubleDot]r\ den\ \
+Graph\ der\ Newton - Interpolation\ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{xnew[j] = xel[j], ynew[j] = yp[0],
+ pro = xel[j] -
+ xp[0], \n\t\tDo[{ynew[j] = ynew[j] + pro*DivDiff[0, i],
+ pro = pro*\((xnew[j] - xp[i])\)}, {i, 1, m}]}, {j, 0,
+ nd}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ Graph\ der\ Newton -
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(newtonplot =
+ ListPlot[Table[{xnew[j], ynew[j]}, {j, 0, nd}],
+ PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{\(-5\), 5}, {\(-1\), 4}}, \tPlotStyle -> Red,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ Nat\[UDoubleDot]rliche\ Spline -
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \
+\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Erstellen\ \
+der\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\n",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \((\
+ Haupt - \ und\ Nebendiagonale\ )\)\ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[{
+ \(\(Du[0] = xp[1] - xp[0];\)\), "\n",
+ \(Do[{Du[k] = xp[k + 1] - xp[k], Dh[k] = 2 \((Du[k - 1] + Du[k])\)}, {k,
+ 1, m - 1}]\)}], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ Cholesky -
+ Zerlegung\ der\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[{
+ \(\(Ch[1] = Sqrt[Dh[1]];\)\), "\n",
+ \(Do[{Cn[k - 1] = Du[k - 1]/Ch[k - 1],
+ Ch[k] = Sqrt[Dh[k] - Cn[k - 1]^2]}, {k, 2, m - 1}]\)}], "Input"],
+
+Cell[BoxData[
+ StyleBox[\(\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Vorw\
+\[ADoubleDot]rtsrechnung\ "\<von oben her\>"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ *) \)\(\n\)\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \tund\ \
+Erstellen\ der\ rechten\ Seite\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \)\),
+
+ FontColor->RGBColor[1, 0, 1]]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[{
+ \(Dv[0] = yp[1] - yp[0]; \ \ \ \ \ \ \ Dv[1] = yp[2] - yp[1];\), "\n",
+ \(\(Dr[1] = 3 \((Dv[1]/Du[1] - Dv[0]/Du[0])\);\)\), "\n",
+ \(\(Z[1] = Dr[1]/Ch[1];\)\), "\n",
+ \(Do[{Dv[k] = yp[k + 1] - yp[k], \n\t\tDr[k] =
+ 3 \((Dv[k]/Du[k] - Dv[k - 1]/Du[k - 1])\), \n\t\tZ[
+ k] = \((Dr[k] - Z[k - 1]*Cn[k - 1])\)/Ch[k]}, \n{k, 2,
+ m - 1}]\)}], "Input"],
+
+Cell[BoxData[
+ StyleBox[\(\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+R\[UDoubleDot]ckw\[ADoubleDot]rtsrechnung\ "\<von unten her\>"\ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ *) \)\(\n\)\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \tBerechnung\ der\ Koeffizienten\ B\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ *) \)\),
+ FontColor->RGBColor[1, 0, 1]]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[{
+ \(B[m] = 0; \ \ B[m - 1] = Z[m - 1]/Ch[m - 1];\), "\n",
+ \(Do[B[k] = \((Z[k] - B[k + 1]*Cn[k])\)/Ch[k], {k, m - 2, 1, \(-1\)}]; \
+ B[0] = 0;\)}], "Input"],
+
+Cell[BoxData[
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \tBerechnung\ der\ \
+Koeffizienten\ A\_\(\(k\)\(\ \)\), \ C\_k\ , \
+ D\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{A[
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+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Entfernen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<L\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m\ \ , \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \
+Einf\[UDoubleDot]gen\ \ eins\ \ Punktes\ \ mit\ \ der\ \ Nummer\ i\ ndex\ \ \ \
+\ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{
+ RowBox[{\(index\ = \ \ 1\ ;\), " ",
+
+ StyleBox[\( (*\
+ Nummer\ des\ einzuf\[UDoubleDot]genden\ Punktes\ \((\
+ index\ )\)\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]]}], " ",
+ "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"If", "[",
+ RowBox[{\(sch \[Equal] "\<E\>"\), ",",
+ RowBox[{"If", "[",
+
+ RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m\), ",",
+ RowBox[{"{",
+
+ RowBox[{\(m = m + 1\),
+ ";", \(Do[{xp[j], yp[j]}, {j, 0, index - 1}]\), ";",
+ "\[IndentingNewLine]",
+ " ", \(Do[{xp[j] = xp[j - 1], yp[j] = yp[j - 1]}, {j,
+ m, index + 1, \(-1\)}]\), ";",
+ "\[IndentingNewLine]",
+ " ", \(xp[index] = \ \ \(-\ 3.75\)\),
+ " ",
+ StyleBox[\( (*\ xp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]",
+ " ", \(yp[index] = \ \ \ 1.0\)}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox[\( (*\ yp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["}",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]]}]}]}]], "Input"],
+
+Cell[BoxData[
+ \(\(nummer[lauf] = m;\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<E\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m, \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \[CapitalADoubleDot]ndern\ des\ Punktes\ mit\ \
+der\ Nummer\ index\ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{
+ RowBox[{\(index\ = \ \ 19\ ;\), " ",
+
+ StyleBox[\( (*\
+ Nummer\ des\ zu\ \[ADoubleDot]ndernden\ Punktes\ \((\
+ index\ )\)\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]]}], " ", "\n", " ",
+ RowBox[{
+ RowBox[{"If", "[",
+ RowBox[{\(sch \[Equal] "\<K\>"\), ",",
+ RowBox[{"If", "[",
+
+ RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m\), ",",
+ RowBox[{"{", " ",
+
+ RowBox[{\(xp[index] = \ \ \ \(-3.90\)\),
+ " ",
+ StyleBox[\( (*\ xp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]",
+ " ", \(yp[index] = \ \ \ \(-0.5\)\)}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox[\( (*\ yp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["}",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]]}]}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<K\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m, \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Bereitstellen\ des\ Parameters\ tp\ f\
+\[UDoubleDot]r\ die\ m\ St\[UDoubleDot]tzpunkte\ \ \ \ \ \ \ \ \ *) \),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\ \)\(\(tp[0] = 0;\)\[IndentingNewLine]
+ Do[{Delt[k - 1] =
+ Sqrt[\((xp[k] - xp[k - 1])\)^2 + \((yp[k] - yp[k - 1])\)^2],
+ tp[k] = tp[k - 1] + Delt[k - 1]}, {k, 1, m}]\)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ St\[UDoubleDot]tzstellen\ f\[UDoubleDot]r\
+\ die\ Parameterdarstellung\ der\ Ellipse\ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ und\ Bereitstellen\ des\ Parameters\
+\ tj, \ \((\ j, \ 0, \ nd\ )\)\ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(nd = 400;\)\)], "Input"],
+
+Cell[BoxData[
+ \(Do[{tj[j] = tp[0] + j*\((tp[m] - tp[0])\)/nd, \
+ tel[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xel[j] = \(-\ 4\)*Cos[tel[j]],
+ yel[j] = 3*Sin[tel[j]]}, {j, 0, nd}]\)], "Input"],
+
+Cell[BoxData[
+ \(<< Graphics`Colors`\)], "Input"],
+
+Cell[BoxData[
+ \(\(liste1 = {Red, HotPink, Green, Apricot, Brown, DarkGreen, Cobalt,
+ Brick, Orange, Magenta, IndianRed, ForestGreen};\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ Plotten\ der\ Ellipse\ \ x\ = \ \(4*
+ cos \((t)\)\ \ und\ \ y\ = \
+ 3*sin \((t)\)\)\ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(ellipsplot =
+ ListPlot[Table[{xel[j], yel[j]}, {j, 0, nd}],
+ PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \tPlotStyle -> Brown,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(punktplot =
+ ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ False, \t
+ PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue,
+ Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5,
+ AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(linienplot =
+ ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ True, \t
+ PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue,
+ Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5,
+ AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(Show[ellipsplot, linienplot, punktplot,
+ Prolog\ -> \ AbsolutePointSize[5]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Newton\ - \
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ *) \),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Funktionsunterprogramm\ zur\ Berechnung\ \
+der\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ \
+Newton - Interpolation\ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], " "}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(FunkDivDiff[xpform_,
+ ypform_] := \ \((\[IndentingNewLine]Do[
+ DivDiffret[k,
+ 1] = \((ypform[k + 1] - ypform[k])\)/\((xpform[k + 1] -
+ xpform[k])\), {k, 0, m - 1}]; \[IndentingNewLine]Do[
+ Do[DivDiffret[k,
+ j] = \((DivDiffret[k + 1, j - 1] -
+ DivDiffret[k, j - 1])\)/\((xpform[k + j] -
+ xpform[k])\), {k, 0, m - j}], {j, 2, m}];
+ DivDiffmatret =
+ Table[DivDiffret[0, j], {j, 1, m}]; {DivDiffmatret})\)\)], "Input"],
+
+Cell[BoxData[
+ \(\(DivDiffxmat = FunkDivDiff[tp, xp]\ ;\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(DivDiffx = DivDiffxmat[\([1]\)];\),
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ x -
+ Werte\ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(DivDiffymat = FunkDivDiff[tp, yp]\ ;\),
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(DivDiffy = DivDiffymat[\([1]\)];\), " ",
+ StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ y -
+ Werte\ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ St\[UDoubleDot]tzstellen\ xj\ und\ yj\ f\
+\[UDoubleDot]r\ den\ Graph\ der\ Newton - Interpolation\ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{xnew[j] = xp[0],
+ prox = tj[j] -
+ tp[0], \[IndentingNewLine]Do[{xnew[j] =
+ xnew[j] + prox*DivDiffx[\([i]\)],
+ prox = prox*\((tj[j] - tp[i])\)}, {i, 1,
+ m}], \[IndentingNewLine]ynew[j] = yp[0],
+ proy = tj[j] - tp[0], \n\t
+ Do[{ynew[j] = ynew[j] + proy*DivDiffy[\([i]\)],
+ proy = proy*\((tj[j] - tp[i])\)}, {i, 1, m}]}, {j, 0,
+ nd}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ Parametrische\ Darstellung\ der\ Newton -
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(newtonplot =
+ ListPlot[Table[{xnew[j], ynew[j]}, {j, 0, nd}],
+ PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \tPlotStyle -> Red,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(\(\(Show[newtonplot, ellipsplot, linienplot, punktplot,
+ Prolog\ -> \ AbsolutePointSize[5]]\)\(\[IndentingNewLine]\)
+ \)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ Nat\[UDoubleDot]rliche\ Spline -
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \
+\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Funktionsunterprogramm\ zur\ Berechnung\ \
+der\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ Koeffizienten\ f\[UDoubleDot]r\ die\ nat\
+\[UDoubleDot]rlichen\ Spline - Interpolation\ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], " "}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{\(FunkNatSpl[xpform_, ypform_]\), ":=", " ",
+ RowBox[{
+ "(", "\[IndentingNewLine]", " ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Erstellen\ \
+der\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\n",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \((\
+ Haupt - \ und\ Nebendiagonale\ )\)\ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ RowBox[{\(Du[0] = xpform[1] - xpform[0]\), ";", "\n",
+ " ", \(Do[{Du[k] = xpform[k + 1] - xpform[k],
+ Dh[k] = 2 \((Du[k - 1] + Du[k])\)}, {k, 1, m - 1}]\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ Cholesky -
+ Zerlegung\ der\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Ch[1] = Sqrt[Dh[1]]\), ";", "\n",
+ " ", \(Do[{Cn[k - 1] = Du[k - 1]/Ch[k - 1],
+ Ch[k] = Sqrt[Dh[k] - Cn[k - 1]^2]}, {k, 2, m - 1}]\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ Vorw\[ADoubleDot]rtsrechnung\ \
+"\<von oben her\>"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["\n",
+ FontColor->RGBColor[1, 0, 1]], " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ und\ Erstellen\ der\ rechten\ \
+Seite\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Dv[0] = ypform[1] - ypform[0]\), ";",
+ " ", \(Dv[1] = ypform[2] - ypform[1]\), ";", "\n",
+ " ", \(Dr[1] = 3 \((Dv[1]/Du[1] - Dv[0]/Du[0])\)\), ";", "\n",
+ " ", \(Z[1] = Dr[1]/Ch[1]\), ";", "\n",
+ " ", \(Do[{Dv[k] = ypform[k + 1] - ypform[k], \n\t\tDr[k] =
+ 3 \((Dv[k]/Du[k] - Dv[k - 1]/Du[k - 1])\), \n\t\tZ[
+ k] = \((Dr[k] - Z[k - 1]*Cn[k - 1])\)/Ch[k]}, \n\ \ \ {k,
+ 2, m - 1}]\), ";", "\[IndentingNewLine]",
+ " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R\[UDoubleDot]ckw\
+\[ADoubleDot]rtsrechnung\ "\<von unten her\>"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["\n",
+ FontColor->RGBColor[1, 0, 1]], " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \tBerechnung\ der\ \
+Koeffizienten\ B\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(B[m] = 0\), ";",
+ " ", \(B[m - 1] = Z[m - 1]/Ch[m - 1]\), ";", "\n",
+ " ", \(Do[
+ B[k] = \((Z[k] - B[k + 1]*Cn[k])\)/Ch[k], {k, m - 2,
+ 1, \(-1\)}]\), ";", " ", \(B[0] = 0\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ Berechnung\ der\ \
+Koeffizienten\ A\_\(\(k\)\(\ \)\), \ C\_k\ , \
+ D\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Do[{A[
+ k] = \((B[k + 1] - B[k])\)/\((3
+ Du[k])\), \n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ Cc[k] =
+ Dv[k]/Du[k] - Du[k]*\((B[k + 1] + 2 B[k])\)/3, \
+ Dc[k] = ypform[k]}, {k, 0, m - 1}]\), ";",
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+ 0.0; \ \ xp[10] = \ \(-1.0\); \ \ \ yp[10] = \(-1.5\); \ \ \ xp[
+ 11] = \(-3.0\); \ \ \ \ \ yp[
+ 11] = \ \(-3.0\); \ \ \ \ \ \ \n\ \ \ \ \ \ xp[
+ 12] = \(-4.5\); \ \ \ \ yp[12] = 0.0;\ \ }];\)\)], "Input"],
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+ PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]\)], "Input"],
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+Cell[BoxData[
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+ StyleBox[\( (*\ \ \ \
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+ Background->RGBColor[0, 1, 0]],
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+ FontColor->RGBColor[1, 0, 0]], " ", "\n",
+ " ", \(If[sch \[Equal] "\<L\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m\ , {m =
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+ FontColor->RGBColor[1, 0, 1]],
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+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
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+Cell[BoxData[
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+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m\ \ , \ \ \ \[IndentingNewLine]TableForm[
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+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
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+Cell[BoxData[
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+ StyleBox[\( (*\ \ \ \ \ \ \
+Einf\[UDoubleDot]gen\ \ eins\ \ Punktes\ \ mit\ \ der\ \ Nummer\ i\ ndex\ \ \ \
+\ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[""], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{\(index\ = \ 17\), ";", " ",
+ StyleBox[\( (*\
+ Nummer\ des\ einzuf\[UDoubleDot]genden\ Punktes\ \((\
+ index\ )\)\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]], " ", "\[IndentingNewLine]",
+
+ RowBox[{"If", "[",
+ RowBox[{\(sch \[Equal] "\<E\>"\), ",",
+ RowBox[{"If", "[",
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+ RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual] m\),
+ ",",
+ RowBox[{"{",
+
+ RowBox[{\(m = m + 1\),
+ ";", \(Do[{xp[j], yp[j]}, {j, 0, index - 1}]\), ";",
+ "\[IndentingNewLine]",
+ " ", \(Do[{xp[j] = xp[j - 1], yp[j] = yp[j - 1]}, {j,
+ m, index + 1, \(-1\)}]\), ";", "\[IndentingNewLine]",
+ " ", \(xp[index] = \ \ \(-4.45\)\),
+ " ",
+ StyleBox[\( (*\ xp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]",
+ " ", \(yp[index] = \ \ \ \(-\ 0.5\)\)}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox[\( (*\ yp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["}",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]]}]}]], "Input"],
+
+Cell[BoxData[
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+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
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+ StyleBox[",",
+ "Subsection",
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+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<E\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m, \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \[CapitalADoubleDot]ndern\ des\ Punktes\ mit\ \
+der\ Nummer\ index\ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{\(index\ = \ \ 1\), " ", ";", " ",
+ StyleBox[\( (*\
+ Nummer\ des\ zu\ \[ADoubleDot]ndernden\ Punktes\ \((\
+ index\ )\)\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]], " ", "\n", " ",
+ RowBox[{"If", "[",
+ RowBox[{\(sch \[Equal] "\<K\>"\), ",",
+ RowBox[{"If", "[",
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+ RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual] m\),
+ ",",
+ RowBox[{"{", " ",
+
+ RowBox[{\(xp[index] = \ \ \ \(-4.45\)\),
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+ StyleBox[\( (*\ xp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]",
+ " ", \(yp[index] = \ 0.5\)}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox[\( (*\ yp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["}",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]]}]}]], "Input"],
+
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+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<K\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m, \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ \(\(nummer[lauf] = m;\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Bereitstellen\ des\ Parameters\ tp\ f\
+\[UDoubleDot]r\ die\ m\ St\[UDoubleDot]tzpunkte\ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\ \)\(\(tp[0] = 0;\)\[IndentingNewLine]
+ Do[{Delt[k - 1] =
+ Sqrt[\((xp[k] - xp[k - 1])\)^2 + \((yp[k] - yp[k - 1])\)^2],
+ tp[k] = tp[k - 1] + Delt[k - 1]}, {k, 1, m}]\)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ St\[UDoubleDot]tzstellen\ f\[UDoubleDot]r\
+\ die\ Parameterdarstellung\ einer\ Acht\ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ und\ Bereitstellen\ des\ Parameters\
+\ tj, \ \((\ j, \ 0, \ nd\ )\)\ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(nd = 400;\)\)], "Input"],
+
+Cell[BoxData[{
+ \(Do[{\
+ tach[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xach[j] = \(-3\)\ Cos[tach[j]] - 1.5,
+ yach[j] = 3*Sin[1.5 tach[j]]}, {j, \(-100\),
+ 100}]\), "\[IndentingNewLine]",
+ \(Do[{\
+ tach[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xach[j] = \(-6\) + \ 3*tach[j],
+ yach[j] = \(-1.5\) xach[j]}, {j, 101,
+ 150}]\), "\[IndentingNewLine]",
+ \(Do[{\
+ tach[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xach[j] = 6\ - \ 3*tach[251 + j],
+ yach[j] =
+ 1.5 xach[j]}, {j, \(-150\), \(-101\)}]\), "\[IndentingNewLine]",
+ \(\ Do[{\
+ tach[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xach[j] =
+ 1.5 + \ 3*Cos[tach[\(-250\) + j]],
+ yach[j] = 3*Sin[1.5 tach[\(-250\) + j]]}, {j, 151, 360}]\)}], "Input"],
+
+Cell[BoxData[
+ \(\(\(\ \)\(Do[
+ tj[j] = tp[0] + j*\((tp[m] - tp[0])\)/nd, {j, 0, nd}];\)\)\)], "Input"],
+
+Cell[BoxData[
+ \(<< Graphics`Colors`\)], "Input"],
+
+Cell[BoxData[
+ \(\(liste1 = {Red, HotPink, Green, Apricot, Brown, DarkGreen, Cobalt,
+ Brick, Orange, Magenta, IndianRed, ForestGreen};\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ Plotten\ der\ \
+Acht\ \ aus\ \ Kreisb\[ODoubleDot]gen\ \ x\ = \ \(3*
+ cos \((t)\)\ \ und\ \ y\ = \ \(3*
+ sin \((t)\)\ und\ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ linearen\ Teilen\ x\ = \ \(-6\) + 3*t\)\)\ , \
+ y\ = \ \(\(-1.5\)*x\ \ \ \ und\ \ x\ = \ 6 - 3*t\)\ , \
+ y\ = \ 1.5*x\ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(achtplot =
+ ListPlot[Table[{xach[j], yach[j]}, {j, \(-146\), 360}],
+ PlotJoined\ \[Rule] True, \n\t
+ PlotRange -> {{\(-6\), 5}, {\(-4\), 4}}, \tPlotStyle -> Brown,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(punktplot =
+ ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ False, \t
+ PlotRange -> {{\(-6\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue,
+ Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5,
+ AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(linienplot =
+ ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ True, \t
+ PlotRange -> {{\(-6\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue,
+ Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5,
+ AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
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+ Prolog\ -> \ AbsolutePointSize[5]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Newton\ - \
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ *) \),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
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+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Funktionsunterprogramm\ zur\ Berechnung\ \
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+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ \
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+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], " "}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(FunkDivDiff[xpform_,
+ ypform_] := \ \((\[IndentingNewLine]Do[
+ DivDiffret[k,
+ 1] = \((ypform[k + 1] - ypform[k])\)/\((xpform[k + 1] -
+ xpform[k])\), {k, 0, m - 1}]; \[IndentingNewLine]Do[
+ Do[DivDiffret[k,
+ j] = \((DivDiffret[k + 1, j - 1] -
+ DivDiffret[k, j - 1])\)/\((xpform[k + j] -
+ xpform[k])\), {k, 0, m - j}], {j, 2, m}];
+ DivDiffmatret =
+ Table[DivDiffret[0, j], {j, 1, m}]; {DivDiffmatret})\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{\(DivDiffxmat = FunkDivDiff[tp, xp]\ ;\), "\n",
+ RowBox[{\(DivDiffx = DivDiffxmat[\([1]\)];\),
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+
+ StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ x \
+- Werte\ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}],
+ "\n", \(DivDiffymat = FunkDivDiff[tp, yp]\ ;\),
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]], "\n",
+ RowBox[{\(DivDiffy = DivDiffymat[\([1]\)];\), " ",
+
+ StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ y \
+- Werte\ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]}],
+ "\[IndentingNewLine]"}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ St\[UDoubleDot]tzstellen\ xj\ und\ yj\ f\
+\[UDoubleDot]r\ den\ Graph\ der\ Newton - Interpolation\ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{xnew[j] = xp[0],
+ prox = tj[j] -
+ tp[0], \[IndentingNewLine]Do[{xnew[j] =
+ xnew[j] + prox*DivDiffx[\([i]\)],
+ prox = prox*\((tj[j] - tp[i])\)}, {i, 1,
+ m}], \[IndentingNewLine]ynew[j] = yp[0],
+ proy = tj[j] - tp[0], \n\t
+ Do[{ynew[j] = ynew[j] + proy*DivDiffy[\([i]\)],
+ proy = proy*\((tj[j] - tp[i])\)}, {i, 1, m}]}, {j, 0,
+ nd}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ Parametrische\ Darstellung\ der\ Newton -
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(newtonplot =
+ ListPlot[Table[{xnew[j], ynew[j]}, {j, 0, nd}],
+ PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{\(-6.0\), 5}, {\(-4\), 4}}, \tPlotStyle -> Red,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(\(\(Show[achtplot, newtonplot, linienplot, punktplot,
+ Prolog\ -> \ AbsolutePointSize[5]]\)\(\[IndentingNewLine]\)
+ \)\)], "Input"],
+
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+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ Periodische\ Spline -
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+\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Funktionsunterprogramm\ zur\ Berechnung\ \
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+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ Koeffizienten\ f\[UDoubleDot]r\ die\ \
+periodischen\ Spline - Interpolation\ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], " "}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
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+ RowBox[{
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+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Erstellen\ der\ \
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+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\n",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \((\
+ Haupt - \ und\ Nebendiagonale\ )\)\ \ \ \ \ \ \ \ \ \ *) \),
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+ RowBox[{\(Du[0] = xpform[1] - xpform[0]\), ";",
+ " ", \(Du[m - 1] = xpform[m] - xpform[m - 1]\), ";",
+ "\[IndentingNewLine]", \(Dh[0] = 2*\((\ Du[m - 1] + Du[0]\ )\)\),
+ ";", "\n",
+ " ", \(Do[{Du[k] = xpform[k + 1] - xpform[k],
+ Dh[k] = 2 \((Du[k - 1] + Du[k])\), Dp[k] = 0}, {k, 1, m - 2}]\),
+ ";", "\[IndentingNewLine]", \(Dp[m - 2] = Du[m - 2]\), ";",
+ " ", \(Dh[m - 1] = 2*\((\ Du[m - 2] + Du[m - 1])\)\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ Cholesky -
+ Zerlegung\ der\ "\<fast\>"\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \
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+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Ch[0] = Sqrt[Dh[0]]\), ";",
+ " ", \(Cp[0] = Du[m - 1]/Ch[0]\), ";", "\n",
+ " ", \(Do[{Cn[k - 1] = Du[k - 1]/Ch[k - 1],
+ Ch[k] = Sqrt[Dh[k] - Cn[k - 1]^2], \ \ \ Cp[
+ k] = \((\ Dp[k] - Cp[k - 1]*Cn[k - 1]\ )\)/Ch[k]}, {k, 1,
+ m - 2}]\), ";", "\[IndentingNewLine]", " ", \(Csum = 0\),
+ ";", " ", \(Do[\ Csum = Csum + Cp[i]^2, {i, 1, m - 2}]\), ";",
+ "\[IndentingNewLine]", " ", \(Cn[m - 2] = Cp[m - 2]\), ";",
+ " ", \(Ch[m - 1] = Sqrt[\ Dh[m - 1] - Csum]\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ Vorw\[ADoubleDot]rtsrechnung\ \
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+ StyleBox["\n",
+ FontColor->RGBColor[1, 0, 1]], " ",
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+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ und\ Erstellen\ der\ rechten\ \
+Seite\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Dv[0] = ypform[1] - ypform[0]\), ";",
+ " ", \(Dv[m - 1] = ypform[m] - ypform[m - 1]\), ";", "\n",
+ " ", \(Dr[0] = 3 \((Dv[0]/Du[0] - Dv[m - 1]/Du[m - 1])\)\), ";",
+ "\n", " ", \(Z[0] = Dr[0]/Ch[0]\), ";", "\n",
+ " ", \(Do[{Dv[k] = ypform[k + 1] - ypform[k], \n\t\tDr[k] =
+ 3 \((Dv[k]/Du[k] - Dv[k - 1]/Du[k - 1])\), \n\t\tZ[
+ k] = \((Dr[k] - Z[k - 1]*Cn[k - 1])\)/
+ Ch[k]}, \n\ \ \ \ \ \ {k, 1, m - 1}]\), ";",
+ "\[IndentingNewLine]", " ", \(Zsum = 0\), ";",
+ " ", \(Do[\ Zsum = Zsum + Cp[i]*Z[i], {i, 0, m - 2}]\), ";",
+ "\[IndentingNewLine]",
+ " ", \(Z[m - 1] = \((\ Dr[m - 1] - Zsum\ )\)/Ch[m - 1]\), ";",
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+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ " ", \(Cp[m - 2] = 0\), ";", "\[IndentingNewLine]",
+ " ", \(B[m - 1] = Z[m - 1]/Ch[m - 1]\), ";", "\n",
+ " ", \(Do[
+ B[k] = \((\ Z[k] - B[k + 1]*Cn[k] - Cp[k]*B[m - 1])\)/Ch[k], {k,
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+ " ", \(B[m] = B[0]\), ";", "\[IndentingNewLine]",
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+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ Berechnung\ der\ \
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+ D\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Do[{A[
+ k] = \((B[k + 1] - B[k])\)/\((3
+ Du[k])\), \n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ Cc[k] =
+ Dv[k]/Du[k] - Du[k]*\((B[k + 1] + 2 B[k])\)/3, \
+ Dc[k] = ypform[k]}, {k, 0, m - 1}]\), ";",
+ "\[IndentingNewLine]",
+ " ", \(Aret = Table[A[k], \ {k, 0, m - 1}]\), ";",
+ " ", \(Bret = Table[B[k], {k, 0, m}]\), ";", " ",
+ "\[IndentingNewLine]", " ", \(Cret = Table[Cc[k], {k, 0, m - 1}]\),
+ ";", " ", \(Dret = Table[Dc[k], {k, 0, m - 1}]\), ";",
+ "\[IndentingNewLine]", \({Aret, Bret, Cret, Dret}\)}],
+ ")"}]}]], "Input"],
+
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+ RowBox[{\(Aperx = ABCDxmat[\([1]\)]\ ;\), " ",
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+ StyleBox[\( (*\
+ Koeffizienen\ Ak\ \ \(f \[UDoubleDot]r\)\ die\ x -
+ Werte\ *) \),
+ FontColor->RGBColor[1, 0, 1],
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+ " ",
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(f \[UDoubleDot]r\),
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox["die",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox["x",
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox["-",
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+ StyleBox["Werte",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}],
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+ StyleBox[" ",
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(f \[UDoubleDot]r\),
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+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["die",
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox[" ",
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+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox["-",
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}],
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+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
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+ StyleBox["Dk",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(f \[UDoubleDot]r\),
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+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox["die",
+ FontColor->RGBColor[1, 0, 1],
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
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+ StyleBox[\( (*\
+ Koeffizienen\ Ak\ \ \(f \[UDoubleDot]r\)\ die\ x -
+ Werte\ *) \),
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox["-",
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+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}],
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}],
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["Dk",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(f \[UDoubleDot]r\),
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["die",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["x",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox["-",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["Werte",
+ FontColor->RGBColor[1, 0, 1],
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+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}], "\[IndentingNewLine]"}]], "Input"],
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+ StyleBox[\( (*\ \ \ \ St\[UDoubleDot]tzstellen\ xj\ und\ yj\ f\
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+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{tint = tp[0], \n\t
+ Do[{Dnt[k] = tp[k + 1] - tp[k],
+ If[\((tj[j] \[GreaterEqual]
+ tint\ )\)\ \[And] \ \ \((tj[j] \[LessEqual]
+ tint + Dnt[k]\ )\), {knt = k, Break[]}\ ,
+ tint = tint + Dnt[k]]}, {k, 0, m - 1}], \n\t
+ Dntmj = tj[j] - tp[knt], \[IndentingNewLine]\ \ \ \ \ xper[j] =
+ Aperx[\([knt + 1]\)]*Dntmj^3 + Bperx[\([knt + 1]\)]*Dntmj^2 +
+ Cperx[\([knt + 1]\)]*Dntmj + Dperx[\([knt + 1]\)]\ , \n\t
+ yper[j] =
+ Apery[\([knt + 1]\)]*Dntmj^3 + Bpery[\([knt + 1]\)]*Dntmj^2 +
+ Cpery[\([knt + 1]\)]*Dntmj + \ \ Dpery[\([knt + 1]\)]\ }, \n\t{j,
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+ StyleBox[
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+ StyleBox[" ",
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+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(persplplot =
+ ListPlot[Table[{xper[j], yper[j]}, {j, 0, nd}],
+ PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{\(-6\), 5}, {\(-4\), 4}}, \tPlotStyle -> Green,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
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+ Prolog\ -> \ AbsolutePointSize[5]]\)], "Input"],
+
+Cell[BoxData[
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+ Show[achtplot, persplplot, newtonplot, linienplot, punktplot,
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+ \(\(liste1 = {Red, HotPink, Green, Apricot, Brown, DarkGreen, Cobalt,
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+ Background->RGBColor[0, 1, 0]],
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+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\(yvek\ // \ MatrixForm\ \ \ , \(\(\ \)\(\ \)\)
+ Kontrollausgabe\),
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsubsection",
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+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
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+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 1]],
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+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
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+ FontColor->RGBColor[1, 0, 1]], " ",
+ StyleBox[\(bvek[5]\ // \ MatrixForm\ \ \ \ , \(\(\ \)\(\ \)\)
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+ FontColor->RGBColor[1, 0, 1]],
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+ "Subsubsection",
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+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
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+Cell[BoxData[
+ \(\(Do[
+ Ninv[k] = SetPrecision[Inverse[Nmat[k]], gen], {k, 1,
+ m}];\)\)], "Input"],
+
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+ FontColor->RGBColor[1, 0, 0]], " ",
+ StyleBox[\(Ninv[5]\ // \ MatrixForm\ , \ \ Kontrollausgabe\),
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+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 1]],
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+
+Cell[BoxData[
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+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 0]], " ",
+ StyleBox[\(cvek[9]\ // \ MatrixForm\ \ \ , \ \ \ Kontrollausgabe\),
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+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsubsection",
+ FontColor->RGBColor[1, 0, 1]],
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+ "Subsubsection",
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+ PlotRange -> {{0, 21}, {\(-210\), 210}},
+ AspectRatio \[Rule]
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+ AxesLabel \[Rule] {\ "\<-> X\>", "\< ^ Y\>"}, \
+ PlotStyle \[Rule] liste1[\([k]\)]\), "]"}]}]}], "}"}],
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+ FontColor->RGBColor[1, 0, 0]]], "Input",
+ Background->RGBColor[0, 1, 0]],
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+ FontColor->RGBColor[1, 0, 0],
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+ 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]],
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+ "}]],
+ RowBox[{
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+ FontColor->RGBColor[1, 0, 0]], " ",
+ StyleBox[\(f\[UDoubleDot]r\ l\ = \
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+ FontColor->RGBColor[1, 0, 0],
+ Background->RGBColor[0, 1, 0]]}],
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+ Background->RGBColor[0, 1, 0]],
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diff --git a/Bachelor/Numerische Mathematik/uni-muenster-skript.pdf b/Bachelor/Numerische Mathematik/uni-muenster-skript.pdf Binary files differnew file mode 100644 index 0000000..f70ec3a --- /dev/null +++ b/Bachelor/Numerische Mathematik/uni-muenster-skript.pdf |
