Wikimore

Summary

This W3C-unspecified diagram was created with Mathematica.

Category:Unspec SVG created with Mathematica#00051102Lagrange%20polynomial.svg

DescriptionLagrange polynomial.svg	English: This image shows, for four points ((−9, 5), (−4, 2), (−1, −2), (7, 9)), the (cubic) interpolation polynomial L(x) (dashed, black), which is the sum of the scaled basis polynomials y1ℓ1(x), y2ℓ2(x), y3ℓ3(x) and y4ℓ4(x) (colors). The interpolation polynomial passes through all four control points, and each scaled basis polynomial passes through its respective control point and is 0 where x corresponds to the other three control points.
Date	26 December 2015
Source	Self-made, based on Image:Lagrangepolys.png
Author	User:Glosser.ca
Other versions	Based on Image:Lagrangepolys.png.

Mathematica Code

colors = ColorData[97] /@ Range[4];
pts = {{\[Minus]9, 5}, {\[Minus]4, 2}, {\[Minus]1, \[Minus]2}, {7, 9}};
{xs, ys} = Transpose[pts];

Basis[pts_, x_] := Times @@ (x - DeleteCases[pts, #])/Times @@ (# - DeleteCases[pts, #]) & /@ pts

Plot[
 {
  Evaluate[ys*Basis[xs, x]],
  Total[ys*Basis[xs, x]]
 }, {x, -9, 7},
 PlotStyle -> {Automatic, Automatic, Automatic, Automatic, Directive[Black, Dashed]},
 Frame -> True,
 Axes -> False,
 ImageSize -> Large,
 GridLines -> Automatic,
 GridLinesStyle -> Directive[LightGray, Dashed],
 PlotStyle -> Thick,
 Epilog -> Table[{PointSize[0.02], ColorData[97][i], Point[pts[[i]]]}, {i,4}],
 PlotLegends -> Placed[
  LineLegend[{
   Subscript[\[ScriptL], 1][x], 
   Subscript[\[ScriptL], 2][x],
   Subscript[\[ScriptL], 3][x], 
   Subscript[\[ScriptL], 4][x],
   L[x]
  }, LegendLayout -> {"Row", 1}],
  Top
 ],
 FrameStyle -> Black
]

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.

Category:License migration redundant#Lagrange%20polynomial.svg Category:GFDL#Lagrange%20polynomial.svg

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	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 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.
	This licensing tag was added to this file as part of the GFDL licensing update.CC BY-SA 3.0truetrue