A local convergence proof for the iterative aggregation method
Jan Mandel,Bohuslav Sekerka +1 more
Reads0
Chats0
TLDR
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
More filters
Dissertation
Algebraic Multigrid for Markov Chains and Tensor Decomposition
TL;DR: Numerical tests show that for certain test problems arising from the discretization of high-dimensional partial differential equations on regular lattices the proposed multilevel method significantly outperforms the standard alternating least squares method when a high level of accuracy is required.
Book ChapterDOI
Some Recent Advances in Multigrid Methods
TL;DR: This chapter presents the basic form of the multigrid algorithm and presents methods based on the concept of decomposition of the space into a number of subspaces, where each subspace is the range of a prolongation mapping of a full rank from a lower dimensional space.
Book ChapterDOI
On multigrid and iterative aggregation methods for nonsymmetric problems
TL;DR: A convergence theorem for two-level iterations with one smoothing step is proved, applied to multigrid methods for elliptic boundary value problems and to iterative aggregation methods for large-scale linear algebraic systems arising from input-output models in economics and from a multi-group approximation of the neutron-diffusion equation in reactor physics.
Journal ArticleDOI
Iterant recombination with one-norm minimization for multilevel Markov chain algorithms via the ellipsoid method
TL;DR: The main purpose of this paper is to investigate whether an iterant recombination approach can be obtained in this way that is competitive in terms of execution time and robustness, and derive formulas for subgradients of the one-norm objective function and the constraint functions.
Journal ArticleDOI
Iterative aggregation-disaggregation method for a transient heat conduction equation of copper
M. Laaraj,K. Rhofir +1 more
TL;DR: In this article, the behavior of iterative aggregation-disaggregation method for a system of differential equations resulting from discretisation of one dimensional transient heat conduction equation of copper using finite difference method is studied.
References
More filters
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.