imported>Dmitrii Kouznetsov |
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| {{Image notes
| | == Summary == |
| |Description=Error of the approximation of the integral
| | Importing file |
| <math>\int_{-1}^1 f(x) {\rm d}x </math> with the <math>N</math>-point Legendre-Gaussian quadrature formula versus number <math>N</math> for the following functions:
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| * <math>f(x)=\sqrt{1-x^2}</math> (red)
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| * <math>f(x)=\frac{1}{1+x^2}</math> (green)
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| * <math>f(x)=\frac{1}{3+x} </math> (blue)
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| * <math>f(x)=x^{16} </math> (black)
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| In the last case, at <math> N>8 </math> the residual would be zero; practically, it is determined by the precision of arithmetic used to perform the evaluation. In this example, long double variables were used.
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| The logarithm of modulus of residual is plotted versus number of points in the quadrature formula. If the residual is positive, the datum is represented with circle; if the residual is negative, the datum is represented with dot. Out of grid, at the bottom of the graphic, the precision of calculus is not sufficient.
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| The following code is used to generate the figure:
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| [[GauLegExample/code]]
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| The figure is intented to be used for article
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| [[Legendre-Gauss Quadrature formula]].
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| |Author= Dmitrii Kouznetsov
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| |Date= 2008
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| |Source=[[GauLegExample/code]]
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| |Country first published in= Japan
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| |Copyright holder= Dmitrii Kouznetsov
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| |Notes=The figure is intented to be used in the article [[Legendre-Gauss Quadrature formula]].
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| |Other versions=}}
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| {{attribution}}
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Latest revision as of 18:58, 11 March 2022
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