Accelerated Newton-GPSS methods for systems of nonlinear equations
By utilising generalized positive-definite and skew-Hermitian splitting (GPSS) iteration as the inner solver of inexact Newton method, a class of inexact Newton-GPSS methods for solving systems of nonlinear equations with positive Jacobian matrices are proposed. We discuss the local and semilocal convergence properties under some proper assumptions. Moreover, an accelerated Newton-GPSS method is established and its convergence behavior is analyzed. Numerical results demonstrate the robustness of our methods.
system of nonlinear equations generalized positive-definite and skew-hermitian splitting inexact newton method convergence property