Abstract:

Based on the lopsided Hermitian／skew-Hermitian (LHSS) iteration methods,a class of NewtonPLHSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobi matrices at the solution points is proposed. Two types of local convergence theorems of this class of inexact Newton methods are given. Numerical results confirm the correctness and effectiveness of the proposed methods.

Key words: Hermitian／skew-Hermitian splitting; inexact Newton methods; nonlinear equations; local convergence theorem