The Newton-arithmetic mean method for the solution of systems of nonlinear equations

This paper is concerned with the development of the Newton–Arithmetic Mean method for large systems of nonlinear equations with block–partitioned jacobian matrix. This method is well suited for implementation on a parallel computer; its degree of decomposition is very high. The convergence of the method is analysed for the class of systems whose jacobian matrix satisfies an affine invariant Lipschitz condition. An estimation of the radius of the attraction ball is given. Special attention is reserved to the case of weakly nonlinear systems. A numerical example highlights some peculiar properties of the method.