Legendre Laguerre and Hermite - Gauss Quadrature

Nodes and weights for Legendre Laguerre and Hermite - Gauss Quadrature
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Updated Sun, 21 Feb 2010 09:39:18 +0000

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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.

Cite As

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. Retrieved .

MATLAB Release Compatibility
Created with R14SP2
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Acknowledgements

Inspired: Nodal DG, Modal DG, Flux Reconstruction (FR/CPR)

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Version Published Release Notes
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