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Home > Publications > Reports > Numerical Analysis and Applied Mathematics (TW)

TW 503

Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad
Rational quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity

Abstract

This paper is concerned with rational Szegö quadrature formulas to approximate integrals of the form

I_μ(f) = ∫_-π^π f(e^iθ)dμ(θ)

by a formula like

I_n(f) = ∑_k=1ⁿ λ_kf(z_k)

where the weights λ_k are carefully chosen on the complex unit circle. It will be shown that for a given set of poles, the quadrature formulas can be chosen to be exact in certain subspaces of rational functions of dimension 2n. Also the problem where one node (Radau) or two nodes (Lobatto) are prefixed will be analyzed and the corresponding rational rational Szegö-Radau and rational Szegö-Lobatto quadrature formulas shall be characterized.

report.pdf (330K) / mailto: A. Bultheel