Convergence of asynchronous Jacobi-Newton-iterations

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 x0 andy0 meet the conditionFx0 ≤ 0 ≤ Fy0. 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.

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