Title: Orthogonal rational functions and interpolatory product rules on the unit circle. I. Recurrence and interpolation
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: 1998
Publisher: Oldenbourg, Munich
Series Title: Analysis vol:18 issue:2 pages:167-183
Abstract: Let R be the space of rational functions with poles among {a_k,1/ã_k:k=0,...,∞} with a_0 = 0 and |a_k|<1, k ≥ 1. We consider sequences {R_n:n=0,...,∞} of nested subspaces with U_{n=0,...,∞} R_n = R. This first part will be concerned with the construction of two distinct orthogonal bases for R. We derive an intertwined recurrence relation for these orthogonal functions which appear as denominators of certain continued fractions. By contraction of these continued fractions, these recurrences are decoupled. It is explained how, with the given problem, one can associate two sequences of interpolation data and it is shown that the approximants of the continued fractions interpolate these data in a multipoint Padé sense. In part II, interpolatory quadrature rules which are exact for all f in Rn are constructed and their convergence is discussed as n → ∞.
ISSN: 0174-4747
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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