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Asymptotic Approximations to the Nodes and Weights of Gauss-Hermite and Gauss-Laguerre Quadratures

Abstract: Asymptotic approximations to the zeros of Hermite and Laguerre polynomials are given, together with methods for obtaining the coefficients in the expansions. These approximations can be used as a stand-alone method of computation of Gaussian quadratures for high enough degrees, with Gaussian weights computed from asymptotic approximations for the orthogonal polynomials. We provide numerical evidence showing that for degrees greater than 100, the asymptotic methods are enough for a double precision accuracy computation (15-16 digits) of the nodes and weights of the Gauss-Hermite and Gauss-Laguerre quadratures.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Studies in Applied Mathematics 140:298-332

Editorial: Blackwell Publishing Ltd

 Fecha de publicación: 01/01/2018

Nº de páginas: 34

Tipo de publicación: Artículo de Revista

 DOI: 10.1111/sapm.12201

ISSN: 0022-2526,1467-9590

Proyecto español: MTM2015-67142-P

Url de la publicación: https://onlinelibrary.wiley.com/doi/abs/10.1111/sapm.12201

Autores/as

TEMME, N.M.