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Abstract: 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)kAkkxk. Building on earlier ideas on residual replacement and on insights in the finite precision behaviour of the Krylov subspace methods, computable error bounds are derived for iterations that involve occasionally replacing the computed residuals by the true residuals, and... (Update)
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BibTeX entry: (Update)
@article{ vandervorst01residual,
author = "Henk A. van der Vorst and Qiang Ye",
title = "Residual Replacement Strategies for {Krylov} Subspace Iterative Methods for the Convergence of True Residuals",
journal = "SIAM Journal on Scientific Computing",
volume = "22",
number = "3",
pages = "835--852",
year = "2001",
url = "citeseer.ist.psu.edu/article/vandervorst99residual.html" }
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