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

We present a variant of the popular BiCGSTAB method for solving nonsymmetri c 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 de gree after the same number of steps, but which also requires fewer matrix-v ector products to generate, on average requiring only 1 + 1/k matvecs per s tep. Empirically, it also seems to be more stable and more quickly converge nt. The new method can be implemented as a k-term recurrence and can be vie wed as a bridge connecting the Arnoldi-based FOM/GMRES methods and the Lanc zos-based BiCGSTAB methods.