A functional approach to the Stein equation

P. A. Fuhrmann

doi:10.1016/j.laa.2010.02.001

A functional approach to the Stein equation

P. A. Fuhrmann

Department of Mathematics

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

9 Scopus citations

Abstract

This paper applies the theory of tensor products of functional models to the study of the Stein equation. We analyse the connections between the Sylvester and Stein equations, as well as those between the Anderson-Jury Bezoutian associated with the polynomial Sylvester equation and the T-Bezoutian associated with the homogeneous polynomial Stein equation. The functional setting allows us to extend the theory of finite section Toeplitz matrices and their inversion.

Original language	English
Pages (from-to)	3031-3071
Number of pages	41
Journal	Linear Algebra and Its Applications
Volume	432
Issue number	12
DOIs	https://doi.org/10.1016/j.laa.2010.02.001
State	Published - 1 Jul 2010

Keywords

Bezoutians
Polynomial models
Stein and Sylvester equations
Tensor products
Toeplitz and Hankel operators

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.2010.02.001

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abstract = "This paper applies the theory of tensor products of functional models to the study of the Stein equation. We analyse the connections between the Sylvester and Stein equations, as well as those between the Anderson-Jury Bezoutian associated with the polynomial Sylvester equation and the T-Bezoutian associated with the homogeneous polynomial Stein equation. The functional setting allows us to extend the theory of finite section Toeplitz matrices and their inversion.",

keywords = "Bezoutians, Polynomial models, Stein and Sylvester equations, Tensor products, Toeplitz and Hankel operators",

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N2 - This paper applies the theory of tensor products of functional models to the study of the Stein equation. We analyse the connections between the Sylvester and Stein equations, as well as those between the Anderson-Jury Bezoutian associated with the polynomial Sylvester equation and the T-Bezoutian associated with the homogeneous polynomial Stein equation. The functional setting allows us to extend the theory of finite section Toeplitz matrices and their inversion.

AB - This paper applies the theory of tensor products of functional models to the study of the Stein equation. We analyse the connections between the Sylvester and Stein equations, as well as those between the Anderson-Jury Bezoutian associated with the polynomial Sylvester equation and the T-Bezoutian associated with the homogeneous polynomial Stein equation. The functional setting allows us to extend the theory of finite section Toeplitz matrices and their inversion.

KW - Bezoutians

KW - Polynomial models

KW - Stein and Sylvester equations

KW - Tensor products

KW - Toeplitz and Hankel operators

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 12

ER -

A functional approach to the Stein equation

Abstract

Keywords

ASJC Scopus subject areas

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