Remarks on orthogonal polynomials and balanced realizations

J. Hoffmann; P. A. Fuhrmann

doi:10.1016/0024-3795(94)90368-9

Remarks on orthogonal polynomials and balanced realizations

J. Hoffmann, P. A. Fuhrmann

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Given a proper antistable rational transfer function g, a balanced realization of g is constructed as a matrix representation of the abstract shift realization introduced by Fuhrmann (1976). The required basis is constructed as a union of sets of polynomials orthogonal with respect to weights given by the squares of the absolute values of minimal degree Schmidt vectors of the corresponding Hankel operators. This extends results of Fuhrmann (1991), obtained in the generic case.

Original language	English
Pages (from-to)	741-776
Number of pages	36
Journal	Linear Algebra and Its Applications
Volume	205-206
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(94)90368-9
State	Published - 1 Jan 1994

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(94)90368-9

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abstract = "Given a proper antistable rational transfer function g, a balanced realization of g is constructed as a matrix representation of the abstract shift realization introduced by Fuhrmann (1976). The required basis is constructed as a union of sets of polynomials orthogonal with respect to weights given by the squares of the absolute values of minimal degree Schmidt vectors of the corresponding Hankel operators. This extends results of Fuhrmann (1991), obtained in the generic case.",

author = "J. Hoffmann and Fuhrmann, {P. A.}",

note = "Funding Information: * Earl Katz Family Chair in Algebraic System Theory. {\textquoteleft}Partially supported by the Israeli Academy of Sciences under grant 249/90 and by GIF under grant I 184.",

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N2 - Given a proper antistable rational transfer function g, a balanced realization of g is constructed as a matrix representation of the abstract shift realization introduced by Fuhrmann (1976). The required basis is constructed as a union of sets of polynomials orthogonal with respect to weights given by the squares of the absolute values of minimal degree Schmidt vectors of the corresponding Hankel operators. This extends results of Fuhrmann (1991), obtained in the generic case.

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Remarks on orthogonal polynomials and balanced realizations

Abstract

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