File:Radial Basis Function Interpolation.svg
Summary
| Description |
English: Interpolation of on the interval [0,1] through 15 equally-spaced sample points using (where ε=3). |
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| Date | ||||
| Source | Own work | |||
| Author | Glosser.ca | |||
| SVG development | Category:Valid SVG created with Mathematica code#Radial%20Basis%20Function%20Interpolation.svg
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| Source code | Mathematica coderbf[\[Epsilon]_, x_] := Exp[-(\[Epsilon] x)^2];
g[x_] := Exp[x Cos[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}]
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=exp(x*cos(3pix))-1,_gaussian.png){kind=small}
See also
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