Convergence of Asynchronous Jacobi-Newton-iterations

摘要

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.