Convergence of asynchronous Jacobi-Newton-iterations

Asynchronous iterations often converge under other conditions than their synchronous counterparts. In this contribution this will be studied for 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) less than or equal to 0 less than or equal to Fy(0). In the paper it will be shown, which modifications are necessary to guarantee a similar convergence behavior of an asynchronous computation.