Legendre Laguerre and Hermite - Gauss Quadrature

バージョン 1.2.0.0 (3.25 KB) 作成者: Geert Van Damme
Nodes and weights for Legendre Laguerre and Hermite - Gauss Quadrature
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更新 2010/2/21

ライセンスの表示

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.

引用

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. 取得済み .

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ヒントを与えたファイル: Nodal DG, Modal DG, Flux Reconstruction (FR/CPR)

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バージョン 公開済み リリース ノート
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