Generalizations of orthogonal polynomials

  • Authors:

  • A. Bultheel;A. Cuyt;W. Van Assche;M. Van Barel;B. Verdonk

  • Affiliations:

  • Department of Computer Science (NALAG), K.U. Leuven, Celestijnenlaan 200 A, B-3001 Leuven, Belgium;Department of Mathematics and Computer Science, Universiteit Antwerpen, Middelheimlaan 1, B-2020 Antwerpen, Belgium;Department of Mathematics, K.U. Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium;Department of Computer Science (NALAG), K.U. Leuven, Celestijnenlaan 200 A, B-3001 Leuven, Belgium;Department of Mathematics and Computer Science, Universiteit Antwerpen, Middelheimlaan 1, B-2020 Antwerpen, Belgium

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
  • Year:
  • 2005

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Abstract

We give a survey of recent generalizations of orthogonal polynomials. That includes multidimensional (matrix and vector orthogonal polynomials) and multivariate versions, multipole (orthogonal rational functions) variants, and extensions of the orthogonality conditions (multiple orthogonality). Most of these generalizations are inspired by the applications in which they are applied. We also give a glimpse of these applications, which are usually generalizations of applications where classical orthogonal polynomials also play a fundamental role: moment problems, numerical quadrature, rational approximation, linear algebra, recurrence relations, and random matrices.