Fast simultaneous orthogonal reduction to triangular matrices

I. V. Oseledets, D. V. Savostyanov, E. E. Tyrtyshnikov

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A new algorithm is presented for simultaneous reduction of a given finite sequence of square matrices to upper triangular matrices by means of orthogonal transformations. The reduction is performed through a series of deflation steps, where each step contains a simultaneous eigenvalue problem being a direct generalization of the generalized eigenvalue problem. To solve the latter, a fast variant of the Gauss-Newton algorithm is proposed with some results on its local convergence properties (quadratic for the exact and linear for the approximate reduction) and numerical examples are provided.

Original languageEnglish
Pages (from-to)316-330
Number of pages15
JournalSIAM Journal on Matrix Analysis and Applications
Issue number2
Publication statusPublished - 2009
Externally publishedYes


  • Convergence estimates
  • Fast algor ithms
  • Simultaneous reduction of matrices


Dive into the research topics of 'Fast simultaneous orthogonal reduction to triangular matrices'. Together they form a unique fingerprint.

Cite this