Block Bidiagonalization Methods for Solving Nonsymmetric Linear Systems with Multiple Right-hand Sides

Many applications require the solution of large nonsymmetric linear systems with multiple right-hand sides. Instead of applying an iterative method to each of these systems individually, it is often more eecient to use a block version of the method that generates iterates for all the systems simultaneously. In this paper, we propose block versions of Galerkin/minimal residual pair of bidiagonalization methods for solving large multiple nonsymmetric linear systems. We show how to incorporate deeation to drop converged linear systems, and describe two adaptive block bidiagonalization algorithms and establish a relationship between their residual norms. We present some numerical results that indicate the block bidiagonalization methods have better practical performance than the block GMRES and block biconjugate gradient methods for the solution of large nonsymmetric linear systems with multiple right-hand sides.