summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/tkz-fct/TKZdoc-fct-interpolation.tex
diff options
context:
space:
mode:
authorKarl Berry <karl@freefriends.org>2020-04-12 21:33:18 +0000
committerKarl Berry <karl@freefriends.org>2020-04-12 21:33:18 +0000
commit81491df570eb67c63542d5033a609bf453ed6e22 (patch)
tree71d747ce98db7c12c482309e3c43805064502153 /Master/texmf-dist/doc/latex/tkz-fct/TKZdoc-fct-interpolation.tex
parent459ff31e0bc16b6adf838e7f1e69050496341559 (diff)
tkz-fct (12apr20)
git-svn-id: svn://tug.org/texlive/trunk@54703 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/tkz-fct/TKZdoc-fct-interpolation.tex')
-rw-r--r--Master/texmf-dist/doc/latex/tkz-fct/TKZdoc-fct-interpolation.tex97
1 files changed, 97 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/tkz-fct/TKZdoc-fct-interpolation.tex b/Master/texmf-dist/doc/latex/tkz-fct/TKZdoc-fct-interpolation.tex
new file mode 100644
index 00000000000..822844b18dd
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-fct/TKZdoc-fct-interpolation.tex
@@ -0,0 +1,97 @@
+%!TEX root = /Users/ego/Boulot/TKZ/tkz-fct/doc-fr/TKZdoc-fct-main.tex
+\subsection{Interpolation}
+
+Il s'agit ici de trouver un polynôme d'interpolation sur l'intervalle $[-1~;~1]$ de la fonction $f$ définie par :
+\[
+ f(x)=\frac{1}{1+8x^2}
+\]
+
+Le polynôme d'interpolation est celui obtenu par la méthode de \tkzimp{Lagrange} :
+\begin{equation*}
+\begin{split}
+ P(x) = &1.000000000-0.0000000072x-7.991424876x^2+0.000001079x^3+62.60245358x^4\\
+ & -0.00004253x^5-444.2347594x^6+0.0007118x^7+ 2516.046396x^8 -0.005795x^9\\ &-10240.01777x^{10} +0.025404x^{11}+28118.29594x^{12} -0.05934x^{13} -49850.83249x^{14} \\
+& +0.08097x^{15}+54061.87086x^{16} -0.055620x^{17} -32356.67279x^{18} +0.015440x^{19}\\
+&+8140.046421x^{20}\\
+\end{split}
+\end{equation*}
+
+Ayant utilisé vingt et un points, le polynôme est de degré $20$. Celui-ci est écrit en utilisant la méthode de \tkzimp{Horner}. Dans un premier temps, on demande à gnuplot de tracer la courbe de f en rouge, enfin on trace le polynôme d'interpolation en bleu. Les points utilisés sont en jaune.
+
+\subsubsection{Le code}
+\begin{tkzexample}[code only]
+\begin{tikzpicture}
+\tkzInit[xmin=-1,xmax=1,ymin=-1.8,ymax=1.2,xstep=0.1,ystep=0.2]
+\tkzGrid
+\tkzAxeXY
+\tkzFct[samples = 400, line width=4pt, color = red,opacity=.5](-1---1){1/(1+8*\x*\x)}
+ \tkzFct[smooth,samples = 400, line width=1pt, color = blue,domain =-1:1]%
+{1.0+((((((((((((((((((((
+ 8140.04642)*\x
+ +0.01544)*\x
+ -32356.67279)*\x
+ -0.05562)*\x
+ +54061.87086)*\x
+ +0.08097)*\x
+ -49850.83249)*\x
+ -0.05934)*\x
+ +28118.29594)*\x
+ +0.02540)*\x
+ -10240.01777)*\x
+ -0.00580)*\x
+ +2516.04640)*\x
+ +0.00071)*\x
+ -444.23476)*\x
+ -0.00004)*\x
+ +62.60245)*\x
+ +0.00000)*\x
+ -7.99142)*\x
+ -0.00000)*\x}
+ \tkzSetUpPoint[size=16,color=black,fill=yellow]
+ \foreach \v in {-1,-0.8,---.,1}{\tkzDefPointByFct[draw](\v)}
+\end{tikzpicture}
+\end{tkzexample}
+
+Le résultat est sur la page suivante où on peut constater le phénomène de \tkzimp{Runge}.
+\subsubsection{la figure}
+
+\begin{sidewaysfigure}[htbp]
+\centering
+\begin{tikzpicture}[scale=.75]
+\tkzInit[xmin=-1,xmax=1,ymin=-1.8,ymax=1.2,xstep=0.1,ystep=0.2]
+\tkzGrid
+\tkzAxeXY
+\tkzFct[samples = 400, line width=4pt, color = red,opacity=.5,domain =-1:1]%
+{1/(1+8*\x*\x)}
+ \tkzFct[samples = 400, line width=1pt, color = blue,domain =-1:1]%
+{1.0+
+((((((((((((((((((((
+ 8140.04642)*\x
+ +0.01544)*\x
+ -32356.67279)*\x
+ -0.05562)*\x
+ +54061.87086)*\x
+ +0.08097)*\x
+ -49850.83249)*\x
+ -0.05934)*\x
+ +28118.29594)*\x
+ +0.02540)*\x
+ -10240.01777)*\x
+ -0.00580)*\x
+ +2516.04640)*\x
+ +0.00071)*\x
+ -444.23476)*\x
+ -0.00004)*\x
+ +62.60245)*\x
+ +0.00000)*\x
+ -7.99142)*\x
+ -0.00000)*\x}
+ \tkzSetUpPoint[size=8,color=black,fill=yellow]
+ \foreach \v in {-1,-0.8,---.,1}%
+ {\tkzDefPointByFct[draw](\v)}
+\end{tikzpicture}
+\caption{Interpolation : $\dfrac{1}{1+8x^2}$}
+\end{sidewaysfigure}
+
+\endinput
+