On asynchronous iterations
نویسندگان
چکیده
Asynchronous iterations arise naturally on parallel computers if one wants to minimize idle times. This paper reviews certain models of asynchronous iterations, using a common theoretical framework. The corresponding convergence theory and various domains of applications are presented. These include nonsingular linear systems, nonlinear systems, and initial value problems. c © 2000 Elsevier Science B.V. All rights reserved.
منابع مشابه
Asynchronous Iterations for Enclosing Solutions Asynchronous Iterations for Enclosing Solutions
We consider asynchronous, parallel iterations for calculating enclosures of solutions of systems of nonlinear equations in IR n. Particularly, we will show how two classical theorems on the monotone convergence of some iterative methods for certain classes of nonlinear equations carry over to the asynchronous case.
متن کاملOn Linear Asynchronous Iterations When the Spectral Radius of the Modulus Matrix Is One on Linear Asynchronous Iterations When the Spectral Radius of the Modulus Matrix Is One
A classical result on linear asynchronous iterations states that convergence occurs if and only if the spectral radius of the modulus matrix is less than 1. The present paper shows that if one introduces very mild restrictions on the admissible asynchronous processes, one gets convergence for a larger class of matrices for which the spectral radius of the modulus matrix is allowed to be equal t...
متن کاملPerformance of Asynchronous Linear Iterations with Random Delays
In this paper we investigate the speedup potential of asynchronous iterative algorithms over their synchronous counterparts for the special case of linear iterations. The space of linear iterations of size two is explored by simulation and analytical methods. We find cases and conditions for high asynchronous speedups. However, averaging asynchronous speedups over the whole set of iteration mat...
متن کاملMore Iterations per Second, Same Quality - Why Asynchronous Algorithms may Drastically Outperform Traditional Ones
In this paper, we consider the convergence of a very general asynchronous-parallel algorithm called ARock [1], that takes many well-known asynchronous algorithms as special cases (gradient descent, proximal gradient, Douglas Rachford, ADMM, etc.). In asynchronous-parallel algorithms, the computing nodes simply use the most recent information that they have access to, instead of waiting for a fu...
متن کاملPerturbation of Parallel Asynchronous Linear Iterations by Floating Point Errors
This paper deals with parallel asynchronous linear iterations perturbed by errors in floating point arithmetic. An original result is presented which permits one to localize the limits of perturbed parallel asynchronous linear iterations. The result is established by using the approximate contraction concept. Simple examples are studied.
متن کامل