A Note on the Block and Seed BiCGSTAB Algorithms for Nonsymmetric Multiple Linear Systems

In this paper we ϐirst give a new derivation of the Bl-BiCGSTAB algorithm for solving block linear systems. This derivation is based only on linear algebra and didn't needs matrix orthogonal polynomials. We also propose a new method for solving linear systems with the same coefϐicient matrix and different right-hand sides. The proposed method is based on the BiCGSTAB algorithm and is especially efϐicient when the right-hand sides vector-columns are closely related. Some numerical examples are reported to illustrate the effectiveness of the proposed methods.