Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509666 | Journal of Computational and Applied Mathematics | 2005 | 39 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
A. Bultheel, A. Cuyt, W. Van Assche, M. Van Barel, B. Verdonk,