Premium
Analysis of Monte Carlo accelerated iterative methods for sparse linear systems
Author(s) -
Benzi Michele,
Evans Thomas M.,
Hamilton Steven P.,
Lupo Pasini Massimiliano,
Slattery Stuart R.
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2088
Subject(s) - mathematics , discretization , monte carlo method , linear system , massively parallel , iterative method , convergence (economics) , mathematical optimization , coefficient matrix , sparse matrix , algorithm , computer science , mathematical analysis , parallel computing , statistics , eigenvalues and eigenvectors , physics , quantum mechanics , economics , economic growth , gaussian
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.