File:Runge's phenomenon in Lagrange polynomials.svg
X=5,6,9,11 Y=12,13,14,16
Summary
| Description |
English: The polynomial interpolation of samples taken from a Gaussian distribution displays significant ringing near the endpoints. |
| Date | |
| Source | Own work |
| Author | Glosser.ca |
| SVG development | |
| Source code | Mathematica codedat = {#, Exp[-#^2/2]} & /@ Range[-5, 5];
{xs, ys} = Transpose[dat];
Basis[pts_, x_] := Times @@ (x - DeleteCases[pts, #])/Times @@ (# - DeleteCases[pts, #]) & /@ pts
f = Total[ys*Basis[xs, x]];
Plot[
{
Exp[-x^2/2],
f
}, {x, -5, 5},
Epilog -> {PointSize[Large], Point[dat]},
PlotRange -> All,
PlotStyle -> Thick,
Frame -> True,
FrameStyle -> Black,
Axes -> False,
GridLines -> Automatic,
GridLinesStyle -> Directive[LightGray, Dashed],
ImageSize -> Large]
|
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