Residual Replacement Strategy for Improving the Maximum Attainable Accuracy of Communication-Avoiding Krylov Subspace Methods.

摘要

The behavior of conventional Krylov Subspace Methods (KSMs) infinite precision arithmetic is a well-studied problem. The finite precision Lanczos process, which drives convergence of these methods, can lead to a significant deviation between the recursively computed residual and the true residual, b - Axk, decreasing the maximum attainable accuracy of the solution. (Van der Vorst and Ye 24) have advocated the use of a residual replacement strategy for KSMs to prevent the accumulation of this error, in which the computed residual is replaced by the true residual at specific iterations chosen such that the Lanczos process is undisturbed.