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Gaussian quadratures for several orthogonal polynomials

version 1.1.0.0 (4.87 KB) by Felipe Uribe
This function calculates the zeros and weights of several orthogonal polynomials

5 Downloads

Updated 17 Oct 2014

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The function calculates the zeros and weights of several orthogonal polynomials to be used in particular numerical integration problems. The quadrature rules implemented are the Hermite (probabilist-type), Hermite (physicist-type), Legendre, Chebyshev and Laguerre.
An interesting contribution is the (probabilist-type) Gauss-Hermite quadrature, which is validated through an example by comparing the results of the numerical integration with the moments of a standard Gaussian variable (see 'examples' section). Furthermore, the function displays two figures, the first shows roots vs. weights, and the second shows the corresponding orthogonal polynomials up to the specified order m.

Finally, it can be seen that other orthogonal polynomials can be easily included in the function (case ...) due to the general implementation of the weight's formula.
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1. Input: * m - number of quadrature points
* type - orthogonal polynomial:
'he_prob': Hermite probabilist
'he_phys': Hermite physicist
'legen' : Legendre
'cheby' : Chebyshev
'lague' : Laguerre
2. Output: * xi - zeros
* w - weights
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Comments and Ratings (2)

fadoua sb

Error using roots (line 27)
Input to ROOTS must not contain NaN
or Inf.

Error in gauss_quad (line 116)
xi = sort(roots(P{m+1}));

Updates

1.1.0.0

Minor changes

MATLAB Release Compatibility
Created with R2013a
Compatible with any release
Platform Compatibility
Windows macOS Linux