A restarted Induced Dimension Reduction method to approximate eigenpairs of large unsymmetric matrices

Reinaldo Astudillo Rengifo, MB van Gijzen

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

This work presents a new algorithm to compute eigenpairs of large unsymmetric matrices. Using the Induced Dimension Reduction method (IDR(ss)), which was originally proposed for solving systems of linear equations, we obtain a Hessenberg decomposition, from which we approximate the eigenvalues and eigenvectors of a matrix. This decomposition has two main advantages. First, IDR(ss) is a short-recurrence method, which is attractive for large scale computations. Second, the IDR(ss) polynomial used to create this Hessenberg decomposition is also used as a filter to discard the unwanted eigenvalues. Additionally, we incorporate the implicitly restarting technique proposed by D.C. Sorensen, in order to approximate specific portions of the spectrum and improve the convergence.
Original languageEnglish
Pages (from-to)24-35
Number of pages12
JournalJournal of Computational and Applied Mathematics
Volume296
DOIs
Publication statusPublished - 2016

Keywords

  • Eigenpairs approximation
  • Induced Dimension Reduction method
  • Implicitly restarting
  • Polynomial filter

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