ML(K)BiCGSTAB: a BiCGSTAB variant based on multiple Lanczos starting vectors

Man Chung Yeung, Tony F. Chan

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


We present a variant of the popular BiCGSTAB method for solving nonsymmetric linear systems. The method, which we denote by ML(k)BiCGSTAB, is derived from a variant of the BiCG method based on a Lanczos process using multiple (k > 1) starting left Lanczos vectors. Compared with the original BiCGSTAB method, our new method produces a residual polynomial which is of lower degree after the same number of steps, but which also requires fewer matrix-vector products to generate, on average requiring only 1 + 1/k matvecs per step. Empirically, it also seems to be more stable and more quickly convergent. The new method can be implemented as a k-term recurrence and can be viewed as a bridge connecting the Arnoldi-based FOM/GMRES methods and the Lanczos-based BiCGSTAB methods.

Original languageEnglish (US)
Pages (from-to)1263-1290
Number of pages28
JournalUnknown Journal
Issue number4
StatePublished - Dec 1999
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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