Weak Semilocal Convergence Conditions for a Two-Step Newton Method in Banach Space

Year 2018, Volume: 1 Issue: 2, 137 - 144, 25.12.2018

İoannis K Argyros Santhosh George

Abstract

We present new sufficient convergence conditions for a two step Newton method (TSNM) to solve nonlinear equations in a Banach space setting. The new conditions depend on the center-Lipschitz constant instead of the Lipschitz constant. This way the applicability of (TSNM) is expanded in cases not covered before. Numerical examples are also provided in this study.

Keywords

Newton's method, Modified Newton's method, Two step Newton method, Banach space, Lipschitz, Semilocal convergence, center-Lipschitz condition

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