A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems

Tony Chan*, Tedd Szeto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We propose a new and more stable variant of the CGS method [27] for solving nonsymmetric linear systems. The method is based on squaring the Composite Step BCG method, introduced recently by Bank and Chan [1,2], which itself is a stabilized variant of BCG in that it skips over steps for which the BCG iterate is not defined and causes one kind of breakdown in BCG. By doing this, we obtain a method (Composite Step CGS or CSCGS) which not only handles the breakdowns described above, but does so with the advantages of CGS, namely, no multiplications by the transpose matrix and a faster convergence rate than BCG. Our strategy for deciding whether to skip a step does not involve any machine dependent parameters and is designed to skip near breakdowns as well as produce smoother iterates. Numerical experiments show that the new method does produce improved performance over CGS on practical problems.

Original languageEnglish (US)
Pages (from-to)17-32
Number of pages16
JournalNumerical Algorithms
Volume7
Issue number1
DOIs
StatePublished - Mar 1 1994

Keywords

  • AMS(MOS) subject classification: 65F10, 65F25
  • Lanczos method
  • breakdowns
  • composite step
  • conjugate gradients squared algorithm

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint Dive into the research topics of 'A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems'. Together they form a unique fingerprint.

Cite this