A local convergence proof for the iterative aggregation method
Jan Mandel,Bohuslav Sekerka +1 more
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In this article, the iterative aggregation method for the solution of a system of linear algebraic equations x = Ax + b, where A ≥ 0, b ≥ 0 and s > 0, and s < s, is proved to be locally convergent.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-06-01 and is currently open access. It has received 42 citations till now. The article focuses on the topics: Local convergence & Iterative method.read more
Citations
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Convergence analysis of an iterative aggregation/disaggregation method for computing stationary probability vectors of stochastic matrices
Ivo Marek,Petr Mayer +1 more
TL;DR: In this paper, an aggregation/disaggregation iterative algorithm for computing stationary probability vectors of stochastic matrices is analyzed and two convergence results are presented: fast, global convergence can be achieved provided that a sufficiently high number of relaxations is performed on the fine level.
Journal ArticleDOI
An iterative aggregation-disaggregation algorithm for solving linear equations
TL;DR: A computational algorithm which iteratively aggregates and disaggregates is shown to converge geometrically to the exact solution of large sets of linear equations.
Book ChapterDOI
Numerical Solution of Large Finite Markov Chains by Algebraic Multigrid Techniques
TL;DR: An error analysis of an efficient multigrid variant of the multiplicative Schwars-iteration method of the replacement process approach developed by Sumita and Rieders is provided.
Journal ArticleDOI
A note on local and global convergence analysis of iterative aggregation–disaggregation methods
Ivo Marek,Ivana Pultarová +1 more
TL;DR: In this paper, the convergence properties of the iterative aggregation-disaggregation method for computing a stationary probability distribution vector of a column stochastic matrix are investigated and a sufficient condition for the local convergence property and the corresponding rate of convergence are established.
Journal ArticleDOI
On a two-level multigrid solution method for finite Markov chains
TL;DR: A two-level algebraic multigrid scheme for computing the stationary distribution of a homogeneous Markov chain with a finite state space is studied and its relationship to an iterative aggregation-disaggregation method is revealed and its local convergence is proved.
References
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Book ChapterDOI
Numerical experiments with a multiple grid and a preconditioned Lanczos type method
P. Wesseling,P. Sonneveld +1 more
Journal ArticleDOI
Convergence of multigrid iterations applied to difference equations
TL;DR: In this article, the authors give convergence criteria for general difference schemes for boundary value problems in Lipschitzian regions, and prove convergence for the multi-grid algorithm with Gauss-Seidel's iteration as smoothing procedure.
Journal ArticleDOI
Acceleration by aggregation of successive approximation methods
TL;DR: Methods of successive approximation for solving linear systems or minimization problems are accelerated by aggregation-disaggregation processes, characterized by means of Galerkin approximations, and this in turn permits analysis of the method.
Journal ArticleDOI
Methods of aggregation
Willard L. Miranker,V.Ya. Pan +1 more
TL;DR: A class of methods for accelerating the convergence of iterative methods for solving linear systems by replacing the given linear system with a derived one of smaller size, the aggregated system is studied.