Journal ArticleDOI
Asynchronous Iterative Methods for Multiprocessors
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TLDR
A class of asynchronous iterative methods is presented for solving a system of equations corresponding to a parallel implementation on a multiprocessor system with no synchronization between cooperating processes to show clearly the advantage of purely asynchronous Iterative methods.Abstract:
: A class of asynchronous iterative methods is presented for solving a system of equations. Existing iterative methods are identified in terms of asynchronous iterations, and new schemes are introduced corresponding to a parallel implementation on a multiprocessor system with no synchronization between cooperating processes. A sufficient condition is given to guarantee the convergence of any asynchronous iterations, and results are extended to include iterative methods with memory. Asynchronous iterative methods are then evaluated from a computational point of view, and bounds are derived for the efficiency. The bounds are compared with actual measurements obtained by running various asynchronous iterations on a multiprocessor, and the experimental results show clearly the advantage of purely asynchronous iterative methods. (Author)read more
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Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
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Distributed asynchronous deterministic and stochastic gradient optimization algorithms
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Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms
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The design and analysis of parallel algorithms
TL;DR: Kurskod av teknisk-naturvetenskapliga fakultetsnämnden Kursplan giltig från: 2012, vecka 10 Ansvarig enhet: Inst för datavetenskap SCB-ämnesrubrik: Informatik/Dataoch systemvetenskapskap Huvudområden och successiv fördjupning.
References
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Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
Journal ArticleDOI
Periodic chaotic relaxation
TL;DR: In this article, the authors generalize two results of that paper concerning periodic chaotic relaxation in which overrelaxation is allowed, and show that the optimum rate of convergence is 0( h 2 ) where h is the mesh length.
Journal ArticleDOI
Contraction en norme vectorielle: Convergence d'iterations chaotiques pour des equations non linéaires de point fixe à plusieurs variables
TL;DR: A survey of results concerning vectorial norms for fixed point problems in several variables can be found in this paper, where the authors focus mainly on the notion of contraction with respect to a vectorial norm which ensures convergence of chaotic iterations.