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Applications and Computation of Orthogonal Polynomials

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

  • Conference proceedings
  • © 1999

Overview

Editors:
  1. Walter Gautschi

    1. Department of Computer Sciences, Purdue University, West Lafayette, USA

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  2. Gerhard Opfer

    1. Institute for Applied Mathematics, University of Hamburg, Hamburg, Germany

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    You can also search for this editor in PubMed   Google Scholar

  3. Gene H. Golub

    1. Computer Science Department, Stanford University, Stanford, USA

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Part of the book series: International Series of Numerical Mathematics (ISNM, volume 131)

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Table of contents (18 papers)

  1. Front Matter

    Pages i-xiii
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  2. The Sensitivity of Least Squares Polynomial Approximation

    • Bernhard Beckermann, Edward B. Saff
    Pages 1-19

  3. Transpose-Free Look-Ahead Algorithms for Lanczos’ Method

    • Claude Brezinski, Michela Redivo-Zaglia
    Pages 21-40

  4. Applications of Anti-Gauss Quadrature Rules in Linear Algebra

    • Daniela Calvetti, Lothar Reichel, Fiorella Sgallari
    Pages 41-56

  5. Stieltjes Polynomials and the Error of Gauss-Kronrod Quadrature Formulas

    • Sven Ehrich
    Pages 57-77

  6. Fast Solution of Confluent Vandermonde-Like Linear Systems Using Polynomial Arithmetic

    • Hans-Jürgen Fischer
    Pages 79-92

  7. On Discrete Polynomial Least-Squares Approximation in Moving Time Windows

    • Erich Fuchs
    Pages 93-107

  8. Quadrature Rules Based on s-Orthogonal Polynomials for Evaluating Integrals with Strong Singularities

    • Laura Gori, Elisabetta Santi
    Pages 109-119

  9. Gegenbauer Weight Functions Admitting L 2 Duffin and Schaeffer Type Inequalities

    • David B. Hunter, Geno Nikolov
    Pages 121-131

  10. Questions Related to Gaussian Quadrature Formulas and Two-Term Recursions

    • Dirk P. Laurie
    Pages 133-144

  11. Construction and Computation of a New Set of Orthogonal Polynomials

    • Shikang Li
    Pages 145-151

  12. Fourier Transforms of Orthogonal Polynomials of Singular Continuous Spectral Measures

    • Giorgio Mantica
    Pages 153-163

  13. On a Sequence of Fast Decreasing Polynomial Operators

    • Hrushikesh N. Mhaskar, Jürgen Prestin
    Pages 165-178

  14. Müntz Orthogonal Polynomials and Their Numerical Evaluation

    • Gradimir V. Milovanović
    Pages 179-194

  15. Positivity of Gauss-Kronrod Formulae for a Certain Ultraspherical Weight Function

    • Knut Petras
    Pages 195-202

  16. A Christoffel-Darboux-Type Formula for Szegö Polynomials and Polynomial Evaluation

    • Michael-Ralf Skrzipek
    Pages 203-216

  17. Applications of Tensor-Valued Tri-Variate Hermite Polynomials and Spherical Harmonics in the Kinetic Theory of Gases

    • Kurt Suchy
    Pages 217-225

  18. Indeterminate Moment Problems and a Conjecture on the Growth of the Entire Functions in the Nevanlinna Parametrization

    • Galliano Valent
    Pages 227-237

  19. Spectral Methods Based on Nonclassical Orthogonal Polynomials

    • J. André C. Weideman
    Pages 239-251

  20. Back Matter

    Pages 253-273
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Keywords

About this book

The workshop on Applications and Computation of Orthogonal Polynomials took place March 22-28, 1998 at the Oberwolfach Mathematical Research Institute. It was the first workshop on this topic ever held at Oberwolfach. There were 46 participants from 13 countries, more than half coming from Germany and the United States, and a substantial number from Italy. A total of 23 plenary lectures were presented and 4 short informal talks. Open problems were discussed during an evening session. This volume contains refereed versions of 18 papers presented at, or submitted to, the conference. The theory of orthogonal polynomials, as a branch of classical analysis, is well established. But orthogonal polynomials play also an important role in many areas of scientific computing, such as least squares fitting, numerical integration, and solving linear algebraic systems. Though the basic tenets have their roots in 19th­ century mathematics, the use of modern computers has required the development and study of new algorithms that are accurate and robust. The computational methods and applications represented in this volume, of necessity, are incomplete, yet sufficiently varied to convey an impression of current activities in this area.

Editors and Affiliations

  • Department of Computer Sciences, Purdue University, West Lafayette, USA

    Walter Gautschi

  • Institute for Applied Mathematics, University of Hamburg, Hamburg, Germany

    Gerhard Opfer

  • Computer Science Department, Stanford University, Stanford, USA

    Gene H. Golub

Bibliographic Information

  • Book Title: Applications and Computation of Orthogonal Polynomials

  • Book Subtitle: Conference at the Mathematical Research Institute Oberwolfach, Germany March 22–28, 1998

  • Editors: Walter Gautschi, Gerhard Opfer, Gene H. Golub

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8685-7

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1999

  • Hardcover ISBN: 978-3-7643-6137-2Published: 01 July 1999

  • Softcover ISBN: 978-3-0348-9728-0Published: 03 October 2013

  • eBook ISBN: 978-3-0348-8685-7Published: 06 December 2012

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: XIII, 273

  • Topics: Mathematical and Computational Engineering, Analysis, Applications of Mathematics

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