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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Estimating equilibrium probabilities for band diagonal Markov chains using aggregation and disaggregation techniques
David F. Rogers,Robert D. Plante +1 more
TL;DR: Experimental test results for several different methods for A/D performed upon general band diagonal Markov chains of the type that may arise in certain inventory, queueing, and manpower planning problems are presented.
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Convergence in Norm of Nonsymmetric Algebraic Multigrid
TL;DR: The first such work is presented, discussing why SPD theory breaks down in the nonsymmetric setting, and developing a general framework for convergence of NS-AMG, one of the fastest numerical methods to solve large sparse linear systems.
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Decompositional Analysis of Kronecker Structured Markov Chains
TL;DR: In this paper, a decompositional iterative method with low memory requirements for the steady-state analysis of Kronecker structured Markov chains is proposed, which is formed by a composition of subsystems.
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Necessary and sufficient local convergence condition of one class of iterative aggregation–disaggregation methods
TL;DR: The local convergence of the algorithm is determined only by the sparsity pattern of the matrix and by the choice of the aggregation groups, and the asymptotic convergence rates of the normalized components of approximations corresponding to particular aggregation groups are introduced.
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Physiology and pathology of iterative aggregation–disaggregation methods
Ivana Pultarová,Ivo Marek +1 more
TL;DR: Characteristics that can help to predict the convergence or divergence of iterative aggregation–disaggregation methods are found.
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.