Legendre Laguerre and Hermite - Gauss Quadrature

Versión 1.2.0.0 (3,25 KB) por Geert Van Damme
Nodes and weights for Legendre Laguerre and Hermite - Gauss Quadrature
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This .zip file contains 3 mfiles for computing the nodes and weights for Legendre Laguerre and Hermite - Gauss Quadrature of any order n.

Contrary to most of the files in use, the included files are all based on a symmetrical companion matrix, the eigenvalues of which are always real and correspond to the roots of the respective polynomials.

Hence, there is a 100% certainty of avoiding complex roots at high orders. It is known that the latter issue often causes huge numerical troubles.

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Geert Van Damme (2024). Legendre Laguerre and Hermite - Gauss Quadrature (https://www.mathworks.com/matlabcentral/fileexchange/26737-legendre-laguerre-and-hermite-gauss-quadrature), MATLAB Central File Exchange. Recuperado .

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Se creó con R14SP2
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Más información sobre Numerical Integration and Differential Equations en Help Center y MATLAB Answers.
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Inspiración para: Nodal DG, Modal DG, Flux Reconstruction (FR/CPR)

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Versión Publicado Notas de la versión
1.2.0.0

Some minor changes to the code's comments.
1.1.0.0

No updates were made. Only the description was changed: it should read "the eigenvalues of the companion matrix" instead of "the roots of the companion matrix". Obviously, a matrix has no roots.
1.0.0.0