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Summary

DescriptionRadial Basis Function Interpolation.svg
English: Interpolation of f ( x ) = exp ⁡ ( x cos ⁡ ( 3 π x ) ) − 1 {\displaystyle f(x)=\exp(x\cos(3\pi x))-1} {\displaystyle f(x)=\exp(x\cos(3\pi x))-1} on the interval [0,1] through 15 equally-spaced sample points using r ( x ) = exp ⁡ ( − ( ε x ) 2 ) {\displaystyle r(x)=\exp(-(\epsilon x)^{2})} {\displaystyle r(x)=\exp(-(\epsilon x)^{2})} (where ε=3).
Date
Source Own work
Author Glosser.ca
SVG development
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The SVG code is valid .
This diagram was created with Mathematica.
This file supersedes the file Radial basis function interpolation, f(x)=exp(x*cos(3pix))-1, gaussian.png. It is recommended to use this file rather than the other one.

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minor quality
Source code
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Mathematica code

rbf[\[Epsilon]_,x_]:=Exp[-(\[Epsilon]x)^2];
g[x_]:=Exp[xCos[3\[Pi]x]];
xs=Range[0,14]/14;
ys=g[xs];
weights[\[Epsilon]_?InexactNumberQ]:=LeastSquares[Outer[rbf[\[Epsilon],Abs[#1-#2]]&,xs,xs],ys];
approx[\[Epsilon]_?InexactNumberQ]:=weights[\[Epsilon]].rbf[\[Epsilon],x-xs];
error[\[Epsilon]_?InexactNumberQ]:=NIntegrate[(g[x]-approx[\[Epsilon]])^2,{x,0,1}];
Plot[{g[x],approx[3]},{x,0,1},Epilog->{PointSize[Medium],Point[{#,g[#]}]&/@xs}]

See also

Radial Basis Function Interpolation Error.svg

Licensing

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w:en:Creative Commons
attribution share alike
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You are free:
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Captions

Interpolation of f(x)=exp(x*cos(3pix))-1 using Gaussian radial basis functions
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Date/TimeThumbnailDimensionsUserComment
current03:52, 14 October 2020 Thumbnail for version as of 03:52, 14 October 2020 720 ×ばつ 496 (82 KB)Rayhem New version incorrect
03:51, 14 October 2020 Thumbnail for version as of 03:51, 14 October 2020 720 ×ばつ 496 (82 KB)Rayhem Thicken frame
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