A functional approach to the Stein equation

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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 languageEnglish
Pages (from-to)3031-3071
Number of pages41
JournalLinear Algebra and Its Applications
Volume432
Issue number12
DOIs
StatePublished - 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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