Jump to content

File:Lagrange polynomials for continuations of sequence 1,2,3.gif

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (1,649 × 959 pixels, file size: 67 KB, MIME type: image/gif)

This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “Lagrange polynomials for continuations of sequence 1,2,3.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Summary

Description
English: Lagrange polynomials and their graphs for ten possible continuations (0 to 9) of the sequence 1,2,3; each polynomial evaluates to 1,2,3, and the continuation at input 1,2,3, and 4, respectively; the "correct" continuation 4 leads to the polynomial of least degree
Date
Source Own work
Author Jochen Burghardt
Lagrange polynomials as txt
                               2  3     2   19  
       1, 2, 3, 0            - - x  + 4x  - -- x + 4 
                               3             3


                               1  3     2   9   
       1, 2, 3, 1            - - x  + 3x  - - x + 3 
                               2            2


                               1  3     2   8   
       1, 2, 3, 2            - - x  + 2x  - - x + 2 
                               3            3


                               1  3    2   5   
       1, 2, 3, 3            - - x  + x  - - x + 1 
                               6           6



       1, 2, 3, 4            x



                             1  3    2   17  
       1, 2, 3, 5            - x  - x  + -- x - 1 
                             6            6


                             1  3     2   14  
       1, 2, 3, 6            - x  - 2x  + -- x - 2 
                             3             3


                             1  3     2   13  
       1, 2, 3, 7            - x  - 3x  + -- x - 3 
                             2             2


                             2  3     2   25  
       1, 2, 3, 8            - x  - 4x  + -- x - 4 
                             3             3


                             5  3     2   61  
       1, 2, 3, 9            - x  - 5x  + -- x - 5 
                             6             6
Gnuplot source
set xrange [0.9:4.1]
  plot           -2./3.*x*x*x +4.*x*x -19./3.*x +4. title "" with lines
replot           -1./2.*x*x*x +3.*x*x  -9./2.*x +3. title "" with lines
replot           -1./3.*x*x*x +2.*x*x  -8./3.*x +2. title "" with lines 
replot           -1./6.*x*x*x    +x*x  -5./6.*x +1. title "" with lines 
replot                                        x     title "" with lines
replot            1./6.*x*x*x    -x*x +17./6.*x -1. title "" with lines
replot            1./3.*x*x*x -2.*x*x +14./3.*x -2. title "" with lines
replot            1./2.*x*x*x -3.*x*x +13./2.*x -3. title "" with lines
replot            2./3.*x*x*x -4.*x*x +25./3.*x -4. title "" with lines
replot            5./6.*x*x*x -5.*x*x +61./6.*x -5. title "" with lines
pause -1

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
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.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

20 December 2011

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current20:00, 7 November 2013Thumbnail for version as of 20:00, 7 November 20131,649 × 959 (67 KB)Jochen BurghardtUser created page with UploadWizard

The following page uses this file:

Global file usage

The following other wikis use this file: