Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights
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Data
2010-12-15
Autores
Bracciali, Cleonice Fátima [UNESP]
Castano-Garcia, Laura
Moreno-Balcazar, Juan J.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Elsevier B.V.
Resumo
We consider the Sobolev inner product< f.g > = integral(1)(-1) f(x)g(x)(1 - x(2))(alpha-1/2) dx + integral f'(x)g'(x)d psi(x), alpha > -1/2,where d(psi) is a measure involving a Gegenbauer weight and with mass points outside the interval (-1, 1). We study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product. We obtain the asymptotics of the largest zeros of these polynomials via a Mehler-Heine type formula. These results are illustrated with some numerical experiments. (C) 2010 Elsevier B.V. All rights reserved.
Descrição
Palavras-chave
Sobolev orthogonal polynomials, Asymptotic, Mehler-Heine type formulas
Como citar
Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 235, n. 4, p. 904-915, 2010.