Divide and conquer method for eigenstructure of quasiseparable matrices using zeroes of rational matrix functions

Y. Eidelman*, I. Haimovici

*Corresponding author for this work

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

3 Scopus citations

Abstract

We study divide and conquer method to compute eigenstructure of matrices with quasiseparable representation. In order to find the eigenstructure of a large matrix A we divide the problem into two problems for smaller sized matrices B and C by using the quasiseparable representation of A. In the conquer step we show that to reconstruct the eigenstructure of A from those of B and C amounts to the study of the eigenstructure of a rational matrix function. For a Hermitian matrix A which is order one quasiseparable we completely solve the eigenproblem.

Original languageEnglish
Title of host publicationA Panorama of Modern Operator Theory and Related Topics
Subtitle of host publicationThe Israel Gohberg Memorial Volume
PublisherSpringer Basel
Pages299-328
Number of pages30
ISBN (Electronic)9783034802215
ISBN (Print)9783034802208
DOIs
StatePublished - 1 Jan 2012

Keywords

  • Divide and conquer
  • Hermitian matrix
  • Quasiseparable
  • Rational matrix function

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