On Single Precision Preconditioners for Krylov Subspace Iterative Methods

Authors:
Hiroto Tadano;Tetsuya Sakurai
Affiliations:
Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501 and Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Japan;Department of Computer Science, University of Tsukuba, Tsukuba, Japan 305-8573 and Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Japan
Venue:
Large-Scale Scientific Computing
Year:
2009

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Abstract

Large sparse linear systems Ax= barise in many scientific applications. Krylov subspace iterative methods are often used for solving such linear systems. Preconditioning techniques are efficient to reduce the number of iterations of Krylov subspace methods. The coefficient matrix of the linear system is transformed into MAor AMin the left or right preconditioning, where Mis a preconditioning matrix. In this paper, we analyze the influence of perturbation in the computation of preconditioning of Krylov subspace methods. We show that the perturbation of preconditioner does not affect the accuracy of the approximate solution when the right preconditioning is used. Some numerical experiments illustrate the influence of preconditioners with single precision arithmetic.