Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms

Ren Cang Li, Qiang Ye

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We present simultaneous reduction algorithms for two (nonsymmetric) matrices A and B to upper Hessenberg and lower Hessenberg forms, respectively. One is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type iteration. The algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi algorithm. We shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output system. It is proved that the model reduction has the desirable moment matching property.

Original languageEnglish
Pages (from-to)139-153
Number of pages15
JournalCommunications in Mathematics and Statistics
Issue number2
StatePublished - Jun 1 2014

Bibliographical note

Publisher Copyright:
© 2014, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.


  • Krylov subspace method
  • Lanczos–Arnoldi iteration
  • Model reduction
  • Simultaneous reductions

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Applied Mathematics


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