We develop n-point optimal derivative-free root finding methods of order 2n, based on the Hermite interpolation, by applying a first-order derivative transformation. Analysis of convergence confirms that the optimal order of convergence of the transformed methods is preserved, according to the conjecture of Kung and Traub. To check the effectiveness and reliability of the newly presented method...

In this research article, we present sixteenth-order iterative method for solving nonlinear equations. The Iterative method has optimal order of convergence sixteen in the sense of Kung-Traub conjecture [1], It means iterative scheme uses five function evaluations to achieve 16(= 25−1) order of convergence. The proposed iterative method utilize one derivative evaluation and weight functions. Nu...

A family of simple derivative-free multipoint iterative methods, based on the interpolating polynomials, for solving nonlinear equations is presented. It is shown that the presented n-point iterative method has the convergence order 2n−1 with n function evaluations per iteration. It is an optimal iterative method in the sense of the Kung-Traub’s conjecture. Numerical examples are included to su...

In this paper, based on Ostrowski’s method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices are 1.682, which is optimal according to Kung and Traub’s conjecture. Numerical comparis...

In this paper, we construct two new families of eighth-order methods for solving simple roots of nonlinear equations by using weight function and interpolation methods. Per iteration in the present methods require three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency indexes are 1.682. Kung and Traub conjectured that an iteration method ...

The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub's conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of t...

This paper constructs a general class of two-point optimal fourthorder methods without memory for locating multiple roots of a nonlinear equation. On the basis of Kung-Traub’s conjecture, we investigate the optimal convergence as well as computational properties for the class. Explicit forms of asymptotic error constants are presented to strongly verify the convergence order. A variety of numer...

Abstract We present a new iterative procedure for solving nonlinear equations with multiple roots high efficiency. Starting from the arithmetic mean of Newton’s and Chebysev’s methods, we generate two-step scheme using weight functions, resulting in family methods that satisfies Kung Traub conjecture, yielding an optimal different choices function. have performed in-depth analysis stability mem...

1Department of Psychiatry, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan 2Institute of Behavioral Medicine, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan 3Institute of Allied Health Sciences, College of Medicine and Hospital, National Cheng Kung University, Tainan, Taiwa...

Abstract Many multipoint iterative methods without memory for solving non-linear equations in one variable are found the literature. In particular, there that provide fourth-order, eighth-order or sixteenth-order convergence using only, respectively, three, four five function evaluations per iteration step, thus supporting Kung-Traub conjecture on optimal order of convergence. This paper shows ...