Searching. Please wait…
1579
37
171
29274
4420
2604
347
391
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.
Authorship: Gil A., Segura J., Temme N.M.,
Fuente: Studies in Applied Mathematics 140:298-332
Publisher: Blackwell Publishing Ltd
Publication date: 01/01/2018
No. of pages: 34
Publication type: Article
DOI: 10.1111/sapm.12201
ISSN: 0022-2526,1467-9590
Spanish project: MTM2015-67142-P
Publication Url: https://onlinelibrary.wiley.com/doi/abs/10.1111/sapm.12201
Citations in Scopus
Citations in Google Scholar
Other metrics in Scopus
Consult in Scopus
Consult in UCrea Read publication
AMPARO GIL GOMEZ
JOSE JAVIER SEGURA SALA
TEMME, N.M.
Back