Residual Replacement Strategies for Krylov Subspace Iterative Methods for the Convergence of True Residuals

Henk A. van der Vorst, Qiang Ye
2000 SIAM Journal on Scientific Computing  
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 OukAkkxk. Building on earlier ideas on residual replacement a n d on insights in the nite 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 they
more » ... iduals, and they are used to monitor the deviation of the two residuals and hence to select residual replacement steps, so that the recurrence relations for the computed residuals, which c o n trol the convergence of the method, are perturbed within safe bounds. Numerical examples are presented to demonstrate the e ectiveness of this new residual replacement s c heme.
doi:10.1137/s1064827599353865 fatcat:3mntql6kz5baxdtxt6hisw43ly