Title: Rates of convergence of multipoint rational approximants and quadrature formulas on the unit circle
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: Jan-1997
Publisher: Elsevier science bv
Series Title: Journal of computational and applied mathematics vol:77 issue:1-2 pages:77-101
Abstract: In this paper, multipoint rational approximants to the Riesz-Herglotz transform of a Borel measure µ, supported on [-π,π] are considered. We give estimates for the rate of convergence of these approximants. These estimates are obtained from the asymptotic behaviour of a sequence of rational functions, orthogonal with respect to µ and having prescribed poles 1/α_k, where {α_k:k=1...∞} is a sequence of complex numbers compactly contained in the open unit disk. As an application we also give the rate of convergence of rational Szegö quadrature formulas for integrals with respect to µ.
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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