File:Runge's phenomenon in Lagrange polynomials.svg
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Size of this PNG preview of this SVG file: 719 × 491 pixels. Other resolutions: 320 × 219 pixels | 640 × 437 pixels | 1,024 × 699 pixels | 1,280 × 874 pixels | 2,560 × 1,748 pixels.
Original file (SVG file, nominally 719 × 491 pixels, file size: 73 KB)
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This file supersedes the file Lagrange polynomial Divergence.jpg. It is recommended to use this file rather than the other one.
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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 genesis |  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
I, the copyright holder of this work, hereby publish it under the following licence:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International licence.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the licence, 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 licence as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:17, 29 April 2016 | | 719 × 491 (73 KB) | wikimediacommons>Rayhem | Add legend |
File usage
The following page uses this file:
