Polynomial Preconditioner for Linear Systems with Multiple Right-Hand Sides and Multiple Shifts

Abstract

Abstract. We consider polynomial preconditioners for block Krylov subspace methods with shift-invariance property for a solver to a shifted linear systems with multiple righthand sides and multiple shifts. In general, polynomial preconditioner for shifted Krylov subspace methods is not necessarily effective from the viewpoint of calculation time. In this paper, we show that applying polynomial preconditioner to block Krylov subspace methods with shift-invariance property is effective from the viewpoint of calculation time for solving shifted linear systems with multiple right-hand sides and multiple shifts.