نتایج جستجو برای: kung traubs conjecture

تعداد نتایج: 37931  

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: :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
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: :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...

T. Lotfi

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 iterate,...

Journal: :Algorithms 2016
Jai Prakash Jaiswal

In the literature, recently, some three-step schemes involving four function evaluations for the solution of multiple roots of nonlinear equations, whose multiplicity is not known in advance, are considered, but they do not agree with Kung–Traub’s conjecture. The present article is devoted to the study of an iterative scheme for approximating multiple roots with a convergence rate of eight, whe...

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.

2015
H Wozniakowski H. Wozniakowski

This paper deals with multipoint iterations without memory for the solution of the nonlinear scalar equation (m) f (x) = 0, m ^ 0. Let P n( ) be the maximal order of iterations which use n evaluations of the function or its derivatives per step. We prove the Kung and Traub conjecture p (0) = 2 n ^ for Hermitian information. We show p (m+l)^p (m) and conjecture P n( ) = 2 . The problem of the ma...

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