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- Title
Newton-Kantorovich Convergence Theorem of a Modified Newton's Method Under the Gamma-Condition in a Banach Space.
- Authors
Chen, M.; Khan, Y.; Wu, Q.; Yildirim, A.
- Abstract
A Newton-Kantorovich convergence theorem of a modified Newton's method having third order convergence is established under the gamma-condition in a Banach space to solve nonlinear equations. It is assumed that the nonlinear operator is twice Fréchet differentiable and satisfies the gamma-condition. We also present the error estimate to demonstrate the efficiency of our approach. A comparison of our numerical results with those obtained by other Newton-Kantorovich convergence theorems shows high accuracy of our results.
- Subjects
KANTOROVICH method; NEWTON-Raphson method; BANACH spaces; NONLINEAR equations; NONLINEAR operator equations
- Publication
Journal of Optimization Theory & Applications, 2013, Vol 157, Issue 3, p651
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-012-0237-9