An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence
نویسندگان
چکیده
منابع مشابه
An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence
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...
متن کاملAn efficient family of weighted-Newton methods with optimal eighth order convergence
Based on Newton’s method, we present a family of three-point iterative methods for solving nonlinear equations. In terms of computational cost, the family requires four function evaluations and has convergence order eight. Therefore, it is optimal in the sense of Kung–Traubhypothesis andhas the efficiency index1.682which is better than that ofNewton’s and many other higher order methods. Some n...
متن کاملA Family of Iterative Methods with Accelerated Eighth-Order Convergence
We propose a family of eighth-order iterative methods without memory for solving nonlinear equations. The new iterative methods are developed by using weight function method and using an approximation for the last derivative, which reduces the required number of functional evaluations per step. Their efficiency indices are all found to be 1.682. Several examples allow us to compare our algorith...
متن کاملThree-step iterative methods with optimal eighth-order convergence
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...
متن کاملA new family of four-step fifteenth-order root-finding methods with high efficiency index
In this paper a new family of fifteenth-order methods with high efficiency index is presented. This family include four evaluations of the function and one evaluation of its first derivative per iteration. Therefore, this family of methods has the efficiency index which equals 1.71877. In order to show the applicability and validity of the class, some numerical examples are discussed.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Numerical Analysis
سال: 2012
ISSN: 1687-9562,1687-9570
DOI: 10.1155/2012/346420