Krylov subspace iterative methods in floating point arithmetic

Question

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.

Answer 1

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.

Answer 2

I think, this one Krylov Subspace Methods in Finite Precision: A Unified Approach, Jens-Peter M. Zemke is also worth reading.