On a class of Newton-like methods for solving nonlinear equations

A new Newton-like method for solving nonlinear equations

This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteratio...

On Some Improved Harmonic Mean Newton-Like Methods for Solving Systems of Nonlinear Equations

In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each iteration. The proposed new scheme does not ...

A Class of Newton-like Methods with Cubic Convergence for Nonlinear Equations

In this paper, we present a new class of Newton-like methods for solving nonlinear equations, which deduces, as particular cases, some known results. It is proved that each method in the family is cubically convergent. A general error analysis is given, and the computational efficiency in term of function evaluations is provided. Several numerical examples are given to illustrate the performanc...

A Class of Iterative Methods for Solving Nonlinear Projection Equations

A class of globally convergent iterative methods for solving nonlinear projection equations is provided under a continuity condition of the mapping F. When Fis pseudomonotone, a necessary and sufficient condition on the nonemptiness of the solution set is obtained.

A Class of Methods for Solving Nonlinear Simultaneous Equations