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File:Runge's phenomenon in Lagrange polynomials.svg

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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
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This diagram was created with Mathematica.
 
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Source code
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Mathematica code

dat = {#, 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]
but from where does the text come ?

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23 April 2016

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Date/TimeThumbnailDimensionsUserComment
current14:47, 29 April 2016Thumbnail for version as of 14:47, 29 April 2016719 × 491 (73 KB)RayhemAdd legend
19:39, 23 April 2016Thumbnail for version as of 19:39, 23 April 2016719 × 449 (67 KB)RayhemUser created page with UploadWizard

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