Is there any work that considers Krylov subspace iterative methods in floating point arithmetic? I'm especially interested in how rounding errors influence the convergence and the accuracy of the solution.
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2 Answers
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Some references on rounding error analysis of Krylov methods:
Gutknecht, Martin H., and Zdenvek Strakos. "Accuracy of two three-term and three two-term recurrences for Krylov space solvers." SIAM Journal on Matrix Analysis and Applications 22.1 (2000): 213-229.
Paige, Christopher C., and Zdenvek Strakos. "Residual and backward error bounds in minimum residual Krylov subspace methods." SIAM Journal on Scientific Computing 23.6 (2002): 1898-1923.
Sleijpen, Gerard LG, and Henk A. Van der Vorst. "Maintaining convergence properties of BiCGstab methods in finite precision arithmetic." Numerical algorithms 10.2 (1995): 203-223.
Strakoš, Zdenek, and Petr Tichý. "On error estimation in the conjugate gradient method and why it works in finite precision computations." Electron. Trans. Numer. Anal 13.56-80 (2002): 8.
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$\begingroup$ Thanks! Especially the last paper is very interesting and exactly what I have searched for. $\endgroup$ Commented Oct 24, 2012 at 18:24
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I think, this one Krylov Subspace Methods in Finite Precision: A Unified Approach, Jens-Peter M. Zemke is also worth reading.
