Title: An interpolation algorithm for orthogonal rational functions
Authors: Van Deun, Joris ×
Bultheel, Adhemar #
Issue Date: Mar-2004
Publisher: Elsevier
Series Title: Journal of computational and applied mathematics vol:164 pages:749-762
Abstract: Let A={α_1,α_2,...} be a sequence of numbers on the extended real line R^ = R ∪ {∞} and μ a positive bounded Borel measure with support in (a subset of) R^. We introduce rational functions φ_n with poles {α_1,...α_n} that are orthogonal with respect to μ (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 {φ_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 Ω_µ of the measure µ. To investigate the applicability of this method, error bounds are derived that show that in most cases the error would become unbounded with increasing n, making the procedure less useful. Some examples serve as illustration.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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