Title: Orthogonal rational functions and quadrature on the unit circle
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: 1992
Publisher: J.C. Baltzer
Series Title: Numerical algorithms vol:3 pages:105-116
Abstract: In this paper we shall be concerned with the problem of approximating the integral I_µ{f} = ∫_{-π}^π f(e^{it})dµ(t), by means of the formula I_n{f} = ∑_{j=1,...,n} A_j^{(n)} f(x_j^{(n)}) where µ is some finite positive measure. We want the approximation to be so that I_n{f} = I_µ{f} for f belonging to certain classes of rational functions with prescribed poles which generalize in a certain sense the space of polynomials. In order to get nodes {x_j^{(n)}} of modulus 1 and positive weights A_j^{(n)}, it will be fundamental to use rational functions orthogonal on the unit circle analogous to Szegö polynomials.
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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