Analysis of Monte Carlo accelerated iterative methods for sparse linear systems. Issue 3 (5th March 2017)

• Record Type: Journal Article
• Authors: Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; Lupo Pasini, Massimiliano; Slattery, Stuart R.
• Is Part Of: Numerical linear algebra with applications. Volume 24:Issue 3(2017:May)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-03-05
• Subjects: iterative methods -- Monte Carlo methods -- preconditioning -- resilience -- Richardson iteration -- sparse approximate inverses -- sparse linear systems; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2088
• Languages: English
• ISSNs: 1070-5325

Abstract

Summary: We consider hybrid deterministic‐stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. These methods are expected to have considerable potential for resiliency to faults when implemented on massively parallel machines. We establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.