imported>Caesar Schinas |
|
| Line 1: |
Line 1: |
| {{Image_Details
| | == 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:
| |
| * <math>f(x)=\sqrt{1-x^2}</math> (red)
| |
| * <math>f(x)=\frac{1}{1+x^2}</math> (green)
| |
| * <math>f(x)=\frac{1}{3+x} </math> (blue)
| |
| * <math>f(x)=x^{16} </math> (black)
| |
| 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.
| |
| | |
| 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.
| |
| | |
| The following code is used to generate the figure:
| |
| | |
| [[GauLegExample/code]]
| |
| | |
| The figure is intented to be used for article
| |
| [[Legendre-Gauss Quadrature formula]].
| |
| |author = Dmitrii Kouznetsov
| |
| |copyright = Dmitrii Kouznetsov
| |
| |source = [[GauLegExample/code]]
| |
| |date-created = 2008
| |
| |pub-country = Japan
| |
| |notes = The figure is intented to be used in the article [[Legendre-Gauss Quadrature formula]].
| |
| |versions =
| |
| }}
| |
| | |
| {{attribution}}
| |
Latest revision as of 19:58, 11 March 2022
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment |
|---|
| current | 19:58, 11 March 2022 |  | 1,044 × 780 (81 KB) | Maintenance script (talk | contribs) | == Summary == Importing file |
You cannot overwrite this file.
File usage
The following 3 pages use this file:
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
