Additive Schwarz Iterations for Markov Chains
نویسندگان
چکیده
منابع مشابه
Additive Schwarz Iterations for Markov Chains
A convergence analysis is presented for additive Schwarz iterations when applied to consistent singular systems of equations of the form Ax = b. The theory applies to singular M -matrices with one-dimensional null space and is applicable in particular to systems representing ergodic Markov chains, and to certain discretizations of partial differential equations. Additive Schwarz can be seen as ...
متن کاملRestricted additive Schwarz methods for Markov chains
The Restricted Additive Schwarz (RAS) method is adapted to the problem of computing the stationary probability distribution vector of large, sparse, irreducible stochastic matrices. Inexact and two-level variants are also considered, as well as acceleration by Krylov subspace methods. The convergence properties are analyzed and extensive numerical experiments aimed at assessing the effect of va...
متن کاملOverlapping Additive and Multiplicative Schwarz Iterations for H-matrices
In recent years, an algebraic framework was introduced for the analysis of convergence of Schwarz methods for the solution of linear systems of the form Ax = b. Within this framework, additive and multiplicative Schwarz were shown to converge when the coefficient matrix A is a nonsingular M -matrix, or a symmetric positive definite matrix. In this paper, these results are extended to the case o...
متن کاملWeighted max norms, splittings, and overlapping additive Schwarz iterations
Weighted max-norm bounds are obtained for Algebraic Additive Schwarz Iterations with overlapping blocks for the solution of Ax = b, when the coefficient matrix A is an M -matrix. The case of inexact local solvers is also covered. These bounds are analogous to those that exist using A-norms when the matrix A is symmetric positive definite. A new theorem concerningP -regular splittings is present...
متن کاملAlgebraic Schwarz Methods for the Numerical Solution of Markov Chains
The convergence of additive and multiplicative Schwarz methods for computing certain characteristics of Markov chains such as stationary probability vectors and mean first passage matrices is studied. Our main result is a convergence theorem for multiplicative Schwarz iterations when applied to singular systems. As a by-product we also obtain a convergence result for alternating iterations. It ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2005
ISSN: 0895-4798,1095-7162
DOI: 10.1137/040616541