An interpolation algorithm for orthogonal rational functions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:164

Article; Proceedings Paper

Van Deun, J ; Bultheel, A

关键词: orthogonal rational functions;    orthogonal polynomials;    three-term recurrence;    interpolation;   

DOI  :  10.1016/S0377-0427(03)00493-X

来源: Elsevier

【 摘 要 】

Let A={alpha(1),alpha(2),...}be a sequence of numbers on the extended real line (R) over cap =Rboolean OR{infinity} and mu a positive bounded Borel measure with support in (a subset of) (R) over cap. We introduce rational functions phi(n) with poles {alpha(1),...alpha(n)} that are orthogonal with respect to mu (if all poles are at infinity, we recover the polynomial situation). It is well known that under certain conditions on the location of the poles, the system {phi(n)} is regular such that the orthogonal functions satisfy a three-term recurrence relation similar to the one for orthogonal polynomials. To compute the recurrence coefficients one can use explicit formulas involving inner products. We present a theoretical alternative to these explicit formulas that uses certain interpolation properties of the Riesz-Herglotz-Nevanlinna transform Omega(mu) of the measure mu. Error bounds are derived and some examples serve as illustration. (C) 2003 Elsevier B.V. All rights reserved.

【 授权许可】

Free