Modified Newton-PSS method to solve nonlinear equations (Q1726478)

Following the considerations of \textit{M. T. Darvishi} and \textit{A. Barati} [Appl. Math. Comput. 187, No. 2, 630--635 (2007; Zbl 1116.65060)], the authors construct a modified Newton method for solving systems of nonlinear equations with positive definite Jacobian matrices. In the two-stage procedure, \(F'(x_k)^{-1}\) is calculated only once at every step, but the modified algorithm has order of convergence three at least, while the Newton method converges quadratically. Under the Hölder continuous condition local convergence theorem is given. The algorithm: MN-PSS (modified Newton-PSS) is described in details. Numerical results are reported to verify the efficiency of the proposed method.