Erratum to: Derivative free algorithm for solving nonlinear equations

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

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

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

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New Efficient Optimal Derivative-Free Method for Solving Nonlinear Equations

In this paper, we suggest a new technique which uses Lagrange polynomials to get derivative-free iterative methods for solving nonlinear equations. With the use of the proposed technique and Steffens on-like methods, a new optimal fourth-order method is derived. By using three-degree Lagrange polynomials with other two-step methods which are efficient optimal methods, eighth-order methods can b...

New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations

A new family of eighth-order derivative-freemethods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured...