Formal orthogonal polynomials and Hankel/Toeplitz duality | Zendy

Adhemar Bultheel | Zendy; Marc Van Barel | Zendy

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Formal orthogonal polynomials and Hankel/Toeplitz duality

Author(s) -

Adhemar Bultheel,

Marc Van Barel

Publication year - 1995

Publication title -

numerical algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.981

H-Index - 64

eISSN - 1572-9265

pISSN - 1017-1398

DOI - 10.1007/bf02140773

Subject(s) - toeplitz matrix , mathematics , hankel matrix , recurrence relation , orthogonal polynomials , unit circle , moment (physics) , classical orthogonal polynomials , generalization , jacobi polynomials , matrix (chemical analysis) , positive definite matrix , gegenbauer polynomials , pure mathematics , algebra over a field , mathematical analysis , eigenvalues and eigenvectors , physics , classical mechanics , quantum mechanics , materials science , composite material

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.status: publishe

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