Transpose-free multiple Lanczos and its application in Padé approximation

Man Chung Yeung, Daniel Boley

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A transpose-free two-sided nonsymmetric Lanczos method is developed for multiple starting vectors on both the left and right. The method is mathematically equivalent to the two-sided methods without look-ahead or deflation steps, but avoids the use of the transpose of the system matrix. The method is applied to the computation of the matrix Padé approximation to a linear dynamical system. The result is a method which can be labeled transpose-free matrix Padé via Lanczos (TFMPVL). Under certain circumstances, TFMPVL will actually reduce the total number of matrix-vector products needed. It is illustrated with some numerical examples.

Original languageEnglish (US)
Pages (from-to)101-127
Number of pages27
JournalJournal of Computational and Applied Mathematics
Volume177
Issue number1
DOIs
StatePublished - May 1 2005

Keywords

  • MPVL method
  • Model reduction
  • Padé approximation
  • TFMPVL method
  • Transpose-free Lanczos method

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