A seed method for solving nonsymmetric linear systems with multiple right-hand sides

We present a seed method for solving large nonsymmetric linear systems with multiple right-hand sides. The method uses a single augmented Krylov subspace corresponding to a seed system as a generator of approximations to the nonseed systems. The residual evaluate of the method is shown, and a new strategy to form a seed system which could supply information shareable among the right-hand sides is given. Numerical experiments indicate that our seed selection strategy is more efficient than two existing strategies and our method has significant time saving compared with the block GMRES method and the GMRES method with a projection process.