On the fast reduction of a quasiseparable matrix to Hessenberg and tridiagonal forms

Yuli Eidelman*, Israel Gohberg, Luca Gemignani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we design a fast new algorithm for reducing an N × N quasiseparable matrix to upper Hessenberg form via a sequence of N - 2 unitary transformations. The new reduction is especially useful when it is followed by the QR algorithm to obtain a complete set of eigenvalues of the original matrix. In particular, it is shown that in a number of cases some recently devised fast adaptations of the QR method for quasiseparable matrices can benefit from using the proposed reduction as a preprocessing step, yielding lower cost and a simplification of implementation.

Original languageEnglish
Pages (from-to)86-101
Number of pages16
JournalLinear Algebra and Its Applications
Volume420
Issue number1
DOIs
StatePublished - 1 Jan 2007

Keywords

  • Eigenvalue computation
  • Hessenberg form
  • QR iteration
  • Quasiseparable matrices
  • Tridiagonal form

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