Relaxation strategies for nested Krylov methods
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摘要
This paper studies computational aspects of Krylov methods for solving linear systems where the matrix–vector products dominate the cost of the solution process because they have to be computed via an expensive approximation procedure. In recent years, so-called relaxation strategies for tuning the precision of the matrix–vector multiplications in Krylov methods have proved to be effective for a range of problems. In this paper, we will argue that the gain obtained from such strategies is often limited. Another important strategy for reducing the work in the matrix–vector products is preconditioning the Krylov method by another iterative Krylov method. Flexible Krylov methods are Krylov methods designed for this situation. We combine these two approaches for reducing the work in the matrix–vector products. Specifically, we present strategies for choosing the precision of the matrix–vector products in several flexible Krylov methods as well as for choosing the accuracy of the variable preconditioner such that the overall method is as efficient as possible. We will illustrate this computational scheme with a Schur-complement system that arises in the modeling of global ocean circulation.
论文关键词:Inexact matrix–vector multiplication,Flexible Krylov methods,Inner-outer iteration,Relaxation strategies,Schur complement
论文评审过程:Received 14 February 2004, Revised 16 June 2004, Available online 2 December 2004.
论文官网地址:https://doi.org/10.1016/j.cam.2004.09.024