ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors

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.