Difference between revisions of "Gaussleg.m"
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| − | + | {{DISPLAYTITLE:gaussleg.m}} __NOTOC__ | |
| + | The function calculates Gauss-Legendre points and weights in [a,b] interval with accuracy order n. Of all existing numerical integration methods, Gauss-Legendre quadrature is one of the most efficient and accurate. | ||
==Syntax== | ==Syntax== | ||
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[x,w]=gaussleg(a,b,n) | [x,w]=gaussleg(a,b,n) | ||
| − | == | + | ==Parameters== |
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a - left edge of the interval | a - left edge of the interval | ||
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resulting grid will be n+1. | resulting grid will be n+1. | ||
| − | == | + | ==Outputs== |
x - Gauss-Legendre points | x - Gauss-Legendre points | ||
w - Gauss-Legendre weights | w - Gauss-Legendre weights | ||
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==Notes== | ==Notes== | ||
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==See also== | ==See also== | ||
| − | [[Kernel_utilities | + | [[arclength.m]], [[get_hull.m]], [[grid_fibon.m]], [[grid_igloo.m]], [[grid_kron.m]], [[grid_plot.m]], [[grid_polar.m]], [[grid_test.m]], [[grid_trian.m]], [[one_vcell_solidangle.m]], [[repulsion.m]], [[shrewd.m]], [[sphtarea.m]], [[sphtrsubd.m]], [[vcell_solidangle.m]], [[voitlander.m]], [[voronoisphere.m]], [[zfs_sampling.m]], [[Kernel_utilities]], [[Appendix I: powder grids]] |
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''Version 2.6, authors: [[Ilya Kuprov]]'' | ''Version 2.6, authors: [[Ilya Kuprov]]'' | ||
Latest revision as of 19:37, 6 June 2026
The function calculates Gauss-Legendre points and weights in [a,b] interval with accuracy order n. Of all existing numerical integration methods, Gauss-Legendre quadrature is one of the most efficient and accurate.
Syntax
[x,w]=gaussleg(a,b,n)
Parameters
a - left edge of the interval
b - right edge of the interval
n - accuracy order, the number of points in the
resulting grid will be n+1.
Outputs
x - Gauss-Legendre points w - Gauss-Legendre weights
Notes
Gauss-Legendre quadratures of order exceeding 50 are numerically unstable, subdivide your interval instead of increasing the accuracy order.
See also
arclength.m, get_hull.m, grid_fibon.m, grid_igloo.m, grid_kron.m, grid_plot.m, grid_polar.m, grid_test.m, grid_trian.m, one_vcell_solidangle.m, repulsion.m, shrewd.m, sphtarea.m, sphtrsubd.m, vcell_solidangle.m, voitlander.m, voronoisphere.m, zfs_sampling.m, Kernel_utilities, Appendix I: powder grids
Version 2.6, authors: Ilya Kuprov
