File:Runge's phenomenon in Lagrange polynomials.svg
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Original file (SVG file, nominally 719 × 491 pixels, file size: 73 KB)
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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 |  This diagram was created with Mathematica. |
| 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]
|
Licensing
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- You are free:
- to share – to copy, distribute and transmit the work
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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.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:47, 29 April 2016 | | 719 × 491 (73 KB) | Rayhem | Add legend |
| 19:39, 23 April 2016 |  | 719 × 449 (67 KB) | Rayhem | User created page with UploadWizard |
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