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Convergence of asynchronous Jacobi–Newton‐iterations
Author(s) -
Schrader Uwe
Publication year - 1999
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199903)6:2<157::aid-nla154>3.0.co;2-q
Subject(s) - asynchronous communication , convergence (economics) , monotonic function , mathematics , computation , newton's method , nonlinear system , function (biology) , regular polygon , convex function , mathematical optimization , computer science , algorithm , mathematical analysis , geometry , computer network , physics , quantum mechanics , evolutionary biology , economics , biology , economic growth
Asynchronous iterations often converge under different conditions than their synchronous counterparts. In this paper we will study the global convergence of Jacobi‐Newton‐like methods for nonlinear equations Fx = 0. It is a known fact, that the synchronous algorithm converges monotonically, if F is a convex M‐function and the starting values x 0 and y 0 meet the condition Fx 0 ≤ 0 ≤ Fy 0 . In the paper it will be shown, which modifications are necessary to guarantee a similar convergence behavior for an asynchronous computation. Copyright © 1999 John Wiley & Sons, Ltd.