NewtonKantorovich Convergence Theorem of a Modified Newtons Method Under the Gamma-Condition in a Banach Space
A NewtonKantorovich convergence theorem of a modified Newtons 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 Frchet 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 NewtonKantorovich convergence theorems shows high accuracy of our results.
newtonkantorovich convergence modified newtons method gamma-condition nonlinear equation frchet differentiable error estimate