Near Best Rational Approximation and Spectral Methods

Polynomial interpolation in Chebyshev points is near best in the sense that the interpolant is close to the true minimax polynomial and gives a very uniform interpolation error. Spectral methods for solving ODEs and boundary value problems implicitly rely on this property. For problems with one or more interior boundary layers, however, polynomials do not perform well. This talk presents a rational generalisation of Chebyshev polynomials which can be used for such problems. A comparison is made between the polynomial and rational case and some examples illustrate the applicability in spectral methods.

Speaker Bio: Joris Van Deun graduated as a Master in Computer Science from the Computer Science Department of the Katholieke Universiteit Leuven in Belgium in 2000 and obtained his Ph.D. in Applied Sciences from the same department in 2004. After two years working as a postdoctoral researcher in Leuven he is currently a postdoc working at the Department of Mathematics and Computer Science at the Universiteit Antwerpen, supported by a grant from the Research Foundation - Flanders. He authored over 20 papers and received research funding from the Institute for the promotion of Innovation by Science and Technology in Flanders and from the Research Foundation - Flanders. His current research interests include special functions and orthogonal polynomials, rational approximation and continued fractions and the numerical integration of oscillatory functions.

Presentation Slides: PDF

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