Newton waveform relaxation method for solving algebraic nonlinear equations

We introduce a new notion for solving algebraic nonlinear equations, which is derived from the well known waveform relaxation iterative method, and is well suited to couple different numerical method for nonlinear equations, such as classical Newton’s method, quasi-Newton method, Conjugate-Gradient method, etc. We show in this paper that the arithmetic obtained by coupling the classical Newton’s method has essential capability for parallel computation and converges globally. Numerical results validate the theoretical analysis very well.