Applications and Computation of Orthogonal Polynomials

Conference at the Mathematical Research Institute Oberwolfach, Germany March 22–28, 1998

AvWalter Gautschi,Gene H. Golub

Inbunden, Engelska, 1999

Del i serien International Series of Numerical Mathematics

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Beskrivning

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 leastsquare approximations, Gauss and related quadrature, iterative methods in linear algebra, the detection of singularities, and integral equations.

Produktinformation

Utgivningsdatum:1999-07-01
Mått:155 x 235 x undefined mm
Format:Inbunden
Språk:Engelska
Serie:International Series of Numerical Mathematics
Antal sidor:273
Förlag:Birkhauser Verlag AG
ISBN:9783764361372

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Innehållsförteckning

The sensitivity of least squares polynomial approximation.- Transpose-free look-ahead algorithms for Lanczos’ method.- Applications of anti-Gauss quadrature rules in linear algebra.- Stieltjes polynomials and the error of Gauss-Kronrod quadrature formulas.- Fast solution of confluent Vandermonde-like linear systems using polynomial arithmetic.- On discrete polynomial least-squares approximation in moving time windows.- Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities.- Gegenbauer weight functions admitting L2 Duffin and Schaeffer type inequalities.- Questions related to Gaussian quadrature formulas and two-term recursions.- Construction and computation of a new set of orthogonal polynomials.- Fourier transforms of orthogonal polynomials of singular continuous spectral measures.- On a sequence of fast decreasing polynomial operators.- Müntz orthogonal polynomials and their numerical evaluation.- Positivity of Gauss-Kronrod formulae for a certain ultraspherical weight function.- A Christoffel-Darboux-type formula for Szegö polynomials and polynomial evaluation.- Applications of tensor-valued tri-variate Hermite polynomials and spherical harmonics in the kinetic theory of gases.- Indeterminate moment problems and a conjecture on the growth of the entire functions in the Nevanlinna parametrization.- Spectral methods based on nonclassical orthogonal polynomials.- Author index.