Semilocal Convergence of a Multi-Step Parametric Family of Iterative Methods

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

On Semilocal Convergence of Inexact Newton Methods

Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...

A Family of Iterative Methods with Accelerated Eighth-Order Convergence

We propose a family of eighth-order iterative methods without memory for solving nonlinear equations. The new iterative methods are developed by using weight function method and using an approximation for the last derivative, which reduces the required number of functional evaluations per step. Their efficiency indices are all found to be 1.682. Several examples allow us to compare our algorith...

Semilocal Convergence of Two Iterative Methods for Simultaneous Computation of Polynomial Zeros

In this paper we study some iterative methods for simultaneous approximation of polynomial zeros. We give new semilocal convergence theorems with error bounds for Ehrlich’s and Nourein’s iterations. Our theorems generalize and improve recent results of Zheng and Huang [J. Comput. Math. 18 (2000), 113– 122], Petković and Herceg [J. Comput. Appl. Math. 136 (2001), 283–307] and Nedić [Novi Sad J. ...

Convergence of iterative methods applied to Burgers-Huxley equation