Algorithm 882: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods

Authors:
Joris van Deun;Karl Deckers;Adhemar Bultheel;J. A. C. Weideman
Affiliations:
Universiteit Antwerpen;Katholieke Universiteit Leuven;Katholieke Universiteit Leuven;University of Stellenbosch
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2008

Citing 13
Cited 8

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Abstract

We present a numerical procedure to compute the nodes and weights in rational Gauss-Chebyshev quadrature formulas. Under certain conditions on the poles, these nodes are near best for rational interpolation with prescribed poles (in the same sense that Chebyshev points are near best for polynomial interpolation). As an illustration, we use these interpolation points to solve a differential equation with an interior boundary layer using a rational spectral method. The algorithm to compute the interpolation points (and, if required, the quadrature weights) is implemented as a Matlab program.