Applications and Computation of Orthogonal Polynomials

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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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.

• Numerical Analysis
• Operator
• Wavelet
• algorithm
• dynamische Systeme
• linear algebra
• orthogonal polynomials

• 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

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