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Preconditioned Krylov subspace methods  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.doi:10.1016/j.crma.2017.01.010 fatcat:krlu2ly6m5csjpmhugtgiu6fy4