Tensored polynomial models

P. A. Fuhrmann; U. Helmke

doi:10.1016/j.laa.2009.09.013

Tensored polynomial models

P. A. Fuhrmann, U. Helmke

Department of Mathematics

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

4 Scopus citations

Abstract

The theme of the present paper is to introduce and study two different versions of tensor products of functional models, one over the underlying field and the other over the corresponding algebra of polynomials, as well as related models based on the Kronecker product of polynomial matrices. In the process, we study the Sylvester equation and its reduction to a polynomial matrix equation. We analyse the relation between the two tensor products and use this to elucidate the role of the Anderson-Jury generalized Bezoutians in this context.

Original language	English
Pages (from-to)	678-721
Number of pages	44
Journal	Linear Algebra and Its Applications
Volume	432
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2009.09.013
State	Published - 15 Jan 2010

Keywords

Bezoutians
Kronecker products
Polynomial models
Sylvester equation
Tensor products

ASJC Scopus subject areas

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

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10.1016/j.laa.2009.09.013

Cite this

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title = "Tensored polynomial models",

abstract = "The theme of the present paper is to introduce and study two different versions of tensor products of functional models, one over the underlying field and the other over the corresponding algebra of polynomials, as well as related models based on the Kronecker product of polynomial matrices. In the process, we study the Sylvester equation and its reduction to a polynomial matrix equation. We analyse the relation between the two tensor products and use this to elucidate the role of the Anderson-Jury generalized Bezoutians in this context.",

keywords = "Bezoutians, Kronecker products, Polynomial models, Sylvester equation, Tensor products",

author = "Fuhrmann, {P. A.} and U. Helmke",

note = "Funding Information: Corresponding author. E-mail address: fuhrmannbgu@gmail.com (P.A. Fuhrmann). 1 Partially supported by the ISF under Grant No. 1282/05. 2 Partially supported by the DFG under Grant HE 1858/12-1.",

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AU - Helmke, U.

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N2 - The theme of the present paper is to introduce and study two different versions of tensor products of functional models, one over the underlying field and the other over the corresponding algebra of polynomials, as well as related models based on the Kronecker product of polynomial matrices. In the process, we study the Sylvester equation and its reduction to a polynomial matrix equation. We analyse the relation between the two tensor products and use this to elucidate the role of the Anderson-Jury generalized Bezoutians in this context.

AB - The theme of the present paper is to introduce and study two different versions of tensor products of functional models, one over the underlying field and the other over the corresponding algebra of polynomials, as well as related models based on the Kronecker product of polynomial matrices. In the process, we study the Sylvester equation and its reduction to a polynomial matrix equation. We analyse the relation between the two tensor products and use this to elucidate the role of the Anderson-Jury generalized Bezoutians in this context.

KW - Bezoutians

KW - Kronecker products

KW - Polynomial models

KW - Sylvester equation

KW - Tensor products

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 2-3

ER -

Tensored polynomial models

Abstract

Keywords

ASJC Scopus subject areas

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