An efficient implementation scheme of the simplified Newton iteration for block systems of nonlinear equations Original Research Article

For the simplified Newton iteration for solving an sm-dimensional block systems of nonlinear equations X=h(A⊗Im)F(X)+Φ, this paper presents a new implementation scheme that possesses good intrinsic parallelism, does not involve any complex operations and inner iteration processes, but has to compute the m×m matrix J2=(f′(Z))2. When {J} is of a certain character, often satisfied in practice by large systems, the paper proves that the computation of J2 requires O(m), at most View the MathML source, operations. Under these circumstances, this implementation scheme is superior.