Generalized Newton Raphsons method free from second derivative

Revision of a Derivative-Free Quasi-Newton Method

A derivative-free Quasi-Newton (DFQN) method previously published [J. Greenstadt, Math. Comp., v. 26, 1972, pp. 145—166] has been revised and simplified. The main modification has the effect of keeping all the successive approximants to the Hessian matrix positive-definite. This, coupled with some improvements in the line search, has enhanced the performance of the method considerably. The resu...

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

Derivative free optimization method

Derivative free optimization (DFO) methods are typically designed to solve optimization problems whose objective function is computed by a “black box”; hence, the gradient computation is unavailable. Each call to the “black box” is often expensive, so estimating derivatives by finite differences may be prohibitively costly. Finally, the objective function value may be computed with some noise, ...

A Ninth-Order Iterative Method Free from Second Derivative for Solving Nonlinear Equations

Abstract In this paper, we study and analyze an iterative method for solving nonlinear equations with ninth order of convergence. The new proposed method is obtained by composing an iterative method obtained in Noor et al. [9] with Newton’s method and approximating the first-appeared derivative in the last step by a combination of already evaluated function values. The convergence analysis of o...

Some variants of Chebyshev-Halley methods free from second derivative

In this paper, we present some new variants of Chebyshev-Halley methods free from second derivative for solving nonlinear equation of the type f(x) = 0, and show that the convergence orders of the proposed methods are three or four. Several numerical examples are given to illustrate the efficiency and performance of the new methods.