Multipreconditioning for nonsymmetric problems: The case of orthomin and biCG

Preconditioned Krylov subspace methods [7] are powerful tools for solving linear systems but sometimes they converge very slowly, and often after a long stagnation. A natural way to fix this is by enlarging the space in which the solution is computed at each iteration. Following this idea, we propose in this note two multipreconditioned algorithms: multipreconditioned orthomin and multipreconditioned biCG, which aim at solving general nonsingular linear systems in a small number of iterations. After describing the algorithms, we illustrate their behaviour on systems arising from the FETI domain decomposition method, where in order to enlarge the search space, each local component in the usual preconditioner is kept as a separate preconditioner.