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

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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