Restricted additive Schwarz methods for Markov chains
نویسندگان
چکیده
منابع مشابه
Restricted 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...
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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 ...
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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 ...
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We consider the solution of the algebraic system of equations which result from the dis-cretization of elliptic equations. A class of multilevel algorithms are studied using the additive Schwarz framework. We establish that, in the general case, the condition number of the iterative operator grows at most linearly with the number of levels. The bound is independent of the mesh sizes and the num...
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In this paper, we introduce a new Schwarz preconditioner and with a new coarse space. We construct the preconditioner by grouping together, in one preconditioner, features from the additive overlapping Schwarz methods, from iterative substructuring methods and from a class of restricted additive Schwarz methods. The preconditioner is symmetric and considered as a symmetrized version of restrict...
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ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2011
ISSN: 1070-5325
DOI: 10.1002/nla.821