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On Newton’s Method for Solving Nonlinear Equations and Function Splitting
Ioannis K. Argyros, Saïd Hilout
Journal:

Numerical Mathematics: Theory, Methods and Applications / Volume 4 / Issue 1 / February 2011

Published online by Cambridge University Press:

28 May 2015, pp. 53-67

Print publication:

February 2011
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We provided in [14] and [15] a semilocal convergence analysis for Newton’s method on a Banach space setting, by splitting the given operator. In this study, we improve the error bounds, order of convergence, and simplify the sufficient convergence conditions. Our results compare favorably with the Newton-Kantorovich theorem for solving equations.

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On Newton’s Method for Solving Nonlinear Equations and Function Splitting