Spectral transformations for Hermitian Toeplitz matrices

Authors:
Leyla Daruis;Javier Hernández;Francisco Marcellán
Affiliations:
Departamento de Análisis Matemático, Universidad de La Laguna, Spain;Departamento de Matemáticas, Universidad Carlos III de Madrid, Spain;Departamento de Matemáticas, Universidad Carlos III de Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 5
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Abstract

In this paper we deal with some perturbations of probability measures supported on the unit circle as well as, in a more general framework, with Hermitian linear functionals. We focus our attention in the Hessenberg matrix associated with the multiplication operator in terms of an orthogonal basis in the linear space of polynomials with complex coefficients. The LU and QR factorizations of such a matrix are introduced. Then, the connection between the above-mentioned perturbations and such factorizations is presented.