Semilocal Convergence Analysis for Two-Step Newton Method under\n Generalized Lipschitz Conditions in Banach Spaces

2018/10/30 by Yonghui Ling, Ling, Yonghui, Juan Liang +1
Mathematics · #Iterative Methods for Nonlinear Equations #Advanced Optimization Algorithms Research #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.1810.12533

Abstract

In the present paper, we consider the semilocal convergence problems of the\ntwo-step Newton method for solving nonlinear operator equation in Banach\nspaces. Under the assumption that the first derivative of the operator\nsatisfies a generalized Lipschitz condition, a new semilocal convergence\nanalysis for the two-step Newton method is presented. The Q-cubic convergence\nis obtained by an additional condition. This analysis also allows us to obtain\nthree important spacial cases about the convergence results based on the\npremises of Kantorovich, Smale and Nesterov-Nemirovskii types. An application\nof our convergence results is to the approximation of minimal positive solution\nfor a nonsymmetric algebraic Riccati equation arising from transport theory.\n

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