Newton–Kantorovich Convergence Theorem of a Modified Newton’s Method Under the Gamma-Condition in a Banach Space
Articles > Article · 2012
Authors: M. CHEN, Y. KHAN, Q. WU, Ahmet YILDIRIM
Journal of Optimization Theory and Applications, Journal Indexed in SCI Expanded, International, WoS, 2012, vol 157, pp 651-662
DOI: 10.1007/s10957-012-0237-9
Summary
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 Fr,chet 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.