نتایج جستجو برای: kung and traub conjecture

تعداد نتایج: 16833838  

Journal: :Algorithms 2016
Fayyaz Ahmad

Kung-Traub conjecture states that an iterative method without memory for finding the simple zero of a scalar equation could achieve convergence order 2d−1, and d is the total number of function evaluations. In an article “Babajee, D.K.R. On the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations, Algorithms 2016, 9, 1, doi:10.3390/a9010001”, the author has shown that Kun...

Journal: :international journal of industrial mathematics 0
t. lotfi department of mathematics, hamedan branch, islamic azad university, hamedan, iran.

in this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable taylor and weight function approximation. the method is based on weerakoon-fernando method [s. weerakoon, g.i. fernando, a variant of newton's method with third-order convergence, appl. math. lett. 17 (2000) 87-93]. the method is optimal, as it needs three evaluations per ite...

Journal: :Int. J. Math. Mathematical Sciences 2012
Rajinder Thukral

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...

Journal: :international journal of industrial mathematics 0
p. ‎bassiri‎ department of mathematics, payame noor university (pnu), p. o. box, 19395-3697, tehran, ‎iran.‎ p. bakhtiari‎‎ young researchers and elite club, hamedan branch, islamic azad university, hamedan, ‎iran. s. abbasbandy‎ department of mathematics, imam khomeini international university, ghazvin, 34149-16818, ‎iran.

in this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. this class includes three parameters. therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. some numerical examples are also ‎presented.‎‎

Journal: :Adv. Numerical Analysis 2012
Rajni Sharma Janak Raj Sharma

We derive a family of eighth-order multipoint methods for the solution of nonlinear equations. In terms of computational cost, the family requires evaluations of only three functions and one first derivative per iteration. This implies that the efficiency index of the present methods is 1.682. Kung and Traub 1974 conjectured that multipoint iteration methods without memory based on n evaluation...

Journal: :Int. J. Math. Mathematical Sciences 2012
D. K. R. Babajee Rajinder Thukral

A one-parameter 4-point sixteenth-order King-type family of iterative methods which satisfy the famous Kung-Traub conjecture is proposed. The convergence of the family is proved, and numerical experiments are carried out to find the best member of the family. In most experiments, the best member was found to be a sixteenth-order Ostrowski-type method.

Journal: :Applied Mathematics and Computation 2010
Liping Liu Xia Wang

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 ...

Journal: :Journal of Mathematical Chemistry 2022

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...

2016
Nusrat Yasmin Fiza Zafar Saima Akram N. Hussain N. Yasmin F. Zafar S. Akram

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...

Journal: :J. Applied Mathematics 2013
Malik Zaka Ullah A. S. Al-Fhaid Fayyaz Ahmad

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...

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