Bisection eigenvalue method for hermitian matrices with quasiseparable representation and a related inverse problem

Y. Eidelman*, I. Haimovici

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We study the bisection method for Hermitian matrices with quasiseparable representations.We extend here our results (published in ETNA, 44, 342–366 (2015)) for quasiseparable matrices of order one to an essentially wider class of matrices with quasiseparable representation of any order. To perform numerical tests with our algorithms we need a set of matrices with prescribed spectrum from which to build their quasiseparable generators, without building the whole matrix. We develop a method to solve this inverse problem. Our algorithm for quasiseparable of Hermitian matrices of any order is used to compute singular values of a matrix A0, in the general case not a Hermitian one, with given quasiseparable representation via definition, i.e., as the eigenvalues of the Hermitian matrix A = A* 0A0. We also show that after the computation of an eigenvalue one can compute the corresponding eigenvector easily. The performance of the developed algorithms is illustrated by a series of numerical tests.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAnalysis and the State Space Approach
PublisherSpringer International Publishing
Pages181-200
Number of pages20
DOIs
StatePublished - 2018

Publication series

NameOperator Theory: Advances and Applications
Volume271
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Bisection
  • Eigenstructure
  • Inverse problem
  • Quasiseparable
  • Sturm property

Fingerprint

Dive into the research topics of 'Bisection eigenvalue method for hermitian matrices with quasiseparable representation and a related inverse problem'. Together they form a unique fingerprint.

Cite this