Computational aspects of pseudospectral Laguerre approximations. (English) Zbl 0708.65072

Computations with Laguerre and Hermite polynomials lead to ill- conditioned algorithms and to underflow and overflow problems, even when the degree of the polynomials is low. In order to avoid these problems, the author introduces an interesting scaling function which limits these phenomena and allows, for instance, the determination of the zeros of \(L_ n^{(\alpha)}(x)\) for large values of the degree n.
Reviewer: L.Gatteschi


65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65D20 Computation of special functions and constants, construction of tables
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
34B05 Linear boundary value problems for ordinary differential equations
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