Abstract
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 language | English (US) |
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Pages (from-to) | 1263-1290 |
Number of pages | 28 |
Journal | Unknown Journal |
Volume | 21 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1999 |
Externally published | Yes |
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics