An analysis of the composite step biconjugate gradient method

R.E. Bank, T.F. Chan

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41 Scopus citations


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. © 1993 Springer-Verlag.
Original languageEnglish
Pages (from-to)295-319
Number of pages25
JournalNumerische Mathematik
Issue number1
StatePublished - 1993
Externally publishedYes

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