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Title: Orthogonal rational functions and modified approximants
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: 1996
Publisher: J.C. Baltzer
Series Title: Numerical algorithms vol:11 issue:1-4 pages:57-69
Conference: location:Luminy, France date:5-10 September 1994
Abstract: Let {a_n:n=0...∞} be a sequence in the open unit disk in the complex plane and let B_0 = 1 and
B_n(z)=∏_{k=0...n} (ã_k/|a_k|)(a_k-z)/(1-ã_kz), n=1,2,...,
(ã_k/|a_k| =-1 when a_k=0). Let µ be a positive Borel measure on the unit circle, and let {φ_n: n=0...∞} be the orthonormal sequence obtained by orthonormalization of the sequence {B_n:n=0...∞} with respect to µ. Let {ψ_n:n=0...∞} be the sequence of associated rational functions. Using the functions φ_n, ψ_n and certain conjugates of them, we obtain modified Padé-type approximants to the function F_µ(z)=∫_{-π...π}((t+z)/(t-z))dµ(θ) (t=e^{iθ}).
URI: 
ISSN: 1017-1398
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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