Abstract
Large sparse linear systems Ax= b arise 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 MA or AM in the left or right preconditioning, where M is 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.
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Tadano, H., Sakurai, T. (2008). On Single Precision Preconditioners for Krylov Subspace Iterative Methods. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_83
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DOI: https://doi.org/10.1007/978-3-540-78827-0_83
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78825-6
Online ISBN: 978-3-540-78827-0
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