Numerische Mathematik

, Volume 66, Issue 1, pp 295–319

An analysis of the composite step biconjugate gradient method

  • Randolph E. Bank
  • Tony F. Chan
Article

DOI: 10.1007/BF01385699

Cite this article as:
Bank, R.E. & Chan, T.F. Numer. Math. (1993) 66: 295. doi:10.1007/BF01385699

Summary

The composite step biconjugate gradient method (CSBCG) is a simple modification of the standard biconjugate gradient algorithm (BCG) which smooths the sometimes erratic convergence of BCG by computing only a subset of the iterates. We show that 2×2 composite steps can cure breakdowns in the biconjugate gradient method caused by (near) singularity of principal submatrices of the tridiagonal matrix generated by the underlying Lanczos process. We also prove a “best approximation” result for the method. Some numerical illustrations showing the effect of roundoff error are given.

Mathematics Subject Classifications (1991)

65N2065F10

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Randolph E. Bank
    • 1
  • Tony F. Chan
    • 2
  1. 1.Department of MathematicsUniversity of California at San DiegoLa JollaUSA
  2. 2.Department of MathematicsUniversity of California at Los AngelesLos AngelesUSA