Complex Jacobi matrices

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:127

Article

Beckermann, B

关键词: difference operator;    complex Jacobi matrix;    formal orthogonal polynomials;    resolvent convergence;    convergence of J-fractions;    Pade approximation;   

DOI  :  10.1016/S0377-0427(00)00492-1

来源: Elsevier

【 摘 要 】

Complex Jacobi matrices play an important role in the study of asymptotics and zero distribution of formal orthogonal polynomials (FOPs). The latter are essential tools in several fields of numerical analysis, for instance in the context of iterative methods for solving large systems of linear equations, or in the study of Pade approximation and Jacobi continued fractions. In this paper we present some known and some new results on FOPs in terms of spectral properties of the underlying (infinite) Jacobi matrix: with a special emphasis to unbounded recurrence coefficients. Were we recover several classical results for real Jacobi matrices. The inverse problem of characterizing properties of the Jacobi operator in terms of FOPs and other solutions of a given three-term recurrence is also investigated. This enables us to give results on the approximation of the resolvent by inverses of finite sections, with applications to the convergence of Pade approximants. (C) 2001 Elsevier Science B.V. All rights reserved. MSC 39A70; 47B39; 41A21; 30B70.

【 授权许可】

Free