File:Lagrange polynomials for continuations of sequence 1,2,3.gif
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Lagrange polynomials for continuations of sequence 1,2,3.gif
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Summary
DescriptionLagrange polynomials for continuations of sequence 1,2,3.gif |
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
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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
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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
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Items portrayed in this file
depicts
some value
20 December 2011
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 01:30, 8 November 2013 | 1,649 × 959 (67 KB) | wikimediacommons>Jochen Burghardt | User created page with UploadWizard |
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