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Asymptotic approximations to the nodes and weights of Gauss-Hermite and Gauss-Laguerre quadratures. (arXiv:1709.09656v1 [math.CA])
来源于:arXiv
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 standalone 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. 查看全文>>