Gaussian quadrature rules with simple node-weight relations
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Data
2001-01-01
Autores
de Andrade, EXL
Bracciali, Cleonice Fátima [UNESP]
Ranga, A. S.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Baltzer Sci Publ Bv
Resumo
In this paper, we consider the symmetric Gaussian and L-Gaussian quadrature rules associated with twin periodic recurrence relations with possible variations in the initial coefficient. We show that the weights of the associated Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 4. We also show that the weights of the associated L-Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 5. Special cases of these quadrature rules are given. Finally, an easy to implement procedure for the evaluation of the nodes is described.
Descrição
Palavras-chave
Orthogonal polynomials, Gaussian quadrature rules, L-Gaussian quadrature rules
Como citar
Numerical Algorithms. Bussum: Baltzer Sci Publ Bv, v. 27, n. 1, p. 61-76, 2001.