Recycling Krylov subspaces for solving linear systems with successively changing right-hand sides arising in model reduction

Abstract

We discuss the numerical solution of successive linear systems of equations , by iterative methods based on recycling Krylov subspaces. We propose various recycling algorithms which are based on the generalized conjugate residual (GCR) method. The recycling algorithms reuse the descent vectors computed while solving the previous linear systems , such that a lot of computational work can be saved when solving the current system Ax = b i . The proposed algorithms are robust for solving sequences of linear systems arising in circuit simulation. Sequences of linear systems need to be solved, e.g., in model order reduction (MOR) for systems with many terminals. Numerical experiments illustrate the efficiency and robustness of the proposed method. © 2011 Springer Science+Business Media B.V.