Nonmonotone derivative-free methods for nonlinear equations

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

یک روش نایکنوای فیلتردار برای حل دستگاه معادلات غیرخطی

In this paper, a new approach is presented for solving nonlinear systems of equations in which a derivative-free nonmonotone strategy is employed. Besides, the new approach is equipped with a filter technique. Using this concept, we store some trial points that are probably ignored by some other line search methods. The new algorithm utilizes the information of existing points in the filter in ...

Nonmonotone globalization of inexact finite-difference Newton-iterative methods for nonlinear equations

In this paper we study nonmonotone globalization techniques, in connection with finite-difference inexact Newton-GMRES methods, for solving large-scale systems of nonlinear equations in the case that the Jacobian matrix is not available. We first define a globalization scheme, which combines nonmonotone watchdog rules and nonmonotone derivative-free line searches, and we prove its global conver...

Spectral residual method without gradient information for solving large-scale nonlinear systems of equations

A fully derivative-free spectral residual method for solving largescale nonlinear systems of equations is presented. It uses in a systematic way the residual vector as a search direction, a spectral steplength that produces a nonmonotone process and a globalization strategy that allows for this nonmonotone behavior. The global convergence analysis of the combined scheme is presented. An extensi...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations