Title: Formal orthogonal polynomials and Hankel/Toeplitz duality
Authors: Bultheel, Adhemar ×
Van Barel, Marc #
Issue Date: 1995
Publisher: J.C. Baltzer
Series Title: Numerical algorithms vol:10 pages:289-335
Abstract: For classical polynomials orthogonal with respect to a positive measure supported on the real line, the moment matrix is Hankel and positive definite. The polynomials satisfy a three term recurrence relation. When the measure is supported on the complex unit circle, the moment matrix is positive definite and Toeplitz. They satisfy a coupled Szegö recurrence relation but also a three term recurrence relation. In this paper we study the generalization for formal polynomials orthogonal with respect to an arbitrary moment matrix and consider arbitrary Hankel and Toeplitz matrices as special cases. The relation with Padé approximation and with Krylov subspace iterative methods is also outlined.
ISSN: 1017-1398
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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