File:Lagrange_polynomial.svg
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Summary
DescriptionLagrange polynomial.svg |
English: This W3C-unspecified diagram was created with Mathematica. |
Date | |
Source | Self-made, based on Image:Lagrangepolys.png |
Author | User:Glosser.ca |
Other versions | Image:Lagrangepolys.png |
Source
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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
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This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
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depicts
26 December 2015
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 18:29, 23 April 2016 | 743 × 503 (85 KB) | Rayhem | Swapped axis for frame; added legend. | |
16:01, 26 December 2015 | 449 × 278 (62 KB) | Rayhem | Added major ticks to axis, removed some of the top/bottom whitespace | ||
13:07, 2 January 2009 | 391 × 390 (100 KB) | Renamed user KdYpUvMgT | |||
20:01, 20 December 2008 | 391 × 390 (101 KB) | Renamed user KdYpUvMgT | {{Information |Description={{en|1=This image shows, for four points ((−9, 5), (−4, 2), (−1, −2), (7, 9)), the (cubic) interpolation polynomial L(x), which is the sum of the scaled basis polynomials y0ℓ0(x), y1ℓ1(x), y2ℓ2(x) and y3ℓ3(x). Th |
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Width | 594.45312pt |
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Height | 402.18063pt |
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