Applications and Computation of Orthogonal Polynomials

by Gautschi, Walter; Golub, Gene H.; Opfer, Gerhard

• ISBN13: 9783764361372
• ISBN10: 3764361379
• Format: Hardcover
• Copyright: 1999-08-01
• Publisher: Birkhauser

Summary

This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation. The applications address problems in applied mathematics as well as problems in engineering and the sciences. Prominent among the former are least-squares approximations, Gauss and related quadrature, iterative methods in linear algebra, the detection of singularities, and integral equations. Applications of the latter kind include the use of wavelets in medical diagnostics and the relevance of orthogonal polynomials in optimal control, dynamical systems, and gas dynamics. Computational methods relate to numerical and symbolic computation and include, in particular, matrix interpretation and convergence, perturbation, and stability analyses of relevant algorithms. Generalizations of orthogonal polynomials are also considered, for example, s-orthogonal, matrix- and tensor-valued, MA¼ntz-type, and complex orthogonal polynomials. This volume is of interest to a wide audience of numerical analysts, engineers, and scientists.

Table of Contents

Preface	ix
Participants	xi
The sensitivity of least squares polynomial approximation	1	(20)
Bernhard Beckermann
Edward B. Saff
Transpose-free look-ahead algorithms for Lanczos'method	21	(20)
Claude Brezinski
Michela Redivo-Zaglia
Applications of anti-Gauss quadrature rules in linear algebra	41	(16)
Daniela Calvetti
Lothar Reichel
Fiorella Sgallari
Stieltjes polynomials and the error of Gauss-Kronrod quadrature formulas	57	(22)
Sven Ehrich
Fast solution of confluent Vandermonde-like linear systems using polynomial arithmetic	79	(14)
Hans-Jurgen Fischer
On discrete polynomial least-squares approximation in moving time windows	93	(16)
Erich Fuchs
Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities	109	(12)
Laura Gori
Elisabetta Santi
Gegenbauer weight functions admitting L2 Duffin and Schaeffer type inequalities	121	(12)
David B. Hunter
Geno Nikolov
Questions related to Gaussian quadrature formulas and two-term recursions	133	(12)
Dirk P. Laurie
Construction and computation of a new set of orthogonal polynomials	145	(8)
Shikang Li
Fourier transforms of orthogonal polynomials of singular continuous spectral measures	153	(12)
Giorgio Mantica
On a sequence of fast decreasing polynomial operators	165	(14)
Hrushikesh N. Mhaskar
Jurgen Prestin
Muntz orthogonal polynomials and their numerical evaluation	179	(16)
Gradimir V. Milovanovic
Positivity of Gauss-Kronrod formulae for a certain ultraspherical weight function	195	(8)
Knut Petras
A Christoffel-Darboux-type formula for Szego polynomials and polynomial evaluation	203	(14)
Michael-Ralf Skrzipek
Applications of tensor-valued tri-variate Hermite polynomials and spherical harmonics in the kinetic theory of gases	217	(10)
Kurt Suchy
Indeterminate moment problems and a conjecture on the growth of the entire functions in the Nevanlinna parametrization	227	(12)
Galliano Valent
Spectral methods based on nonclassical orthogonal polynomials	239	(14)
J. Andre C. Weideman
Author index	253	(4)
Subject index	257