Residual and Backward Error Bounds in Minimum Residual Krylov Subspace Methods
نویسندگان
چکیده
منابع مشابه
Residual and Backward Error Bounds in Minimum Residual Krylov Subspace Methods
Minimum residual norm iterative methods for solving linear systems Ax = b can be viewed as, and are often implemented as, sequences of least squares problems involving Krylov subspaces of increasing dimensions. The minimum residual method (MINRES) [C. Paige and M. Saunders, SIAM J. Numer. Anal., 12 (1975), pp. 617–629] and generalized minimum residual method (GMRES) [Y. Saad and M. Schultz, SIA...
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Recent results on residual smoothing are reviewed, and it is observed that certain of these are equivalent to results obtained by different means that relate “peaks” and “plateaus” in residual norm sequences produced by certain pairs of Krylov subspace methods.
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Recent results have demonstrated the performance benefits of communicationavoiding Krylov subspace methods, variants which use blocking strategies to perform O(s) computation steps of the algorithm for each communication step. This allows an O(s) reduction in total communication cost, which can lead to significant speedups on modern computer architectures. Despite potential performance benefits...
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In this paper, a strategy is proposed for alternative computations of the residual vectors in Krylov subspace methods, which improves the agreement of the computed residuals and the true residuals to the level of O(u)‖A‖‖x‖. Building on earlier ideas on residual replacement and on insights in the finite precision behavior of the Krylov subspace methods, computable error bounds are derived for i...
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The behavior of conventional Krylov Subspace Methods (KSMs) in nite precision arithmetic is a well-studied problem. The nite precision Lanczos process, which drives convergence of these methods, can lead to a signi cant deviation between the recursively computed residual and the true residual, b − Ax, decreasing the maximum attainable accuracy of the solution. Van der Vorst and Ye [24] have adv...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2002
ISSN: 1064-8275,1095-7197
DOI: 10.1137/s1064827500381239