A Class of Optimal Eighth-Order Steffensen-Type Iterative Methods for Solving Nonlinear Equations and their Basins of Attraction
نویسندگان
چکیده
منابع مشابه
New eighth-order iterative methods for solving nonlinear equations
In this paper, three new families of eighth-order iterative methods for solving simple roots of nonlinear equations are developed by using weight function methods. Per iteration these iterative methods require three evaluations of the function and one evaluation of the first derivative. This implies that the efficiency index of the developed methods is 1.682, which is optimal according to Kung ...
متن کاملA Family of Optimal Derivative Free Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
In this paper, modification of Steffensen’s method with eight-order convergence is presented. We propose a family of optimal three-step methods with eight-order convergence for solving the simple roots of nonlinear equations by using the weight function and interpolation methods. Per iteration this method requires four evaluations of the function which implies that the efficiency index of the d...
متن کاملSolving Nonlinear Equations Using Steffensen-Type Methods With Optimal Order of Convergence
The author would like to express his deep gratitude to F. Soleymani for his comments which resulted in considerable improvement in the quality of this paper. Thus, he is much grateful for A.E.Alamir for his helpful hints and a great deal of patience in reviewing this paper. The author is also thankful to the reviewer for his constructive remarks and suggestions which have enhanced the present p...
متن کاملCorrigendum to "Basins of attraction for optimal eighth-order methods to find simple roots of nonlinear equations"
Several optimal eighth order methods to obtain simple roots are analyzed. The methods are based on two step, fourth order optimal methods and a third step of modified Newton. The modification is performed by taking an interpolating polynomial to replace either f ðznÞ or f ðznÞ. In six of the eight methods we have used a Hermite interpolating polynomial. The other two schemes use inverse interpo...
متن کاملA Class of Iterative Methods for Solving Nonlinear Equations with Optimal Fourth-order Convergence
In this paper we construct a new third-order iterative method for solving nonlinear equations for simple roots by using inverse function theorem. After that a class of optimal fourth-order methods by using one function and two first derivative evaluations per full cycle is given which is obtained by improving the existing third-order method with help of weight function. Some physical examples a...
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: Applied Mathematics & Information Sciences
سال: 2016
ISSN: 1935-0090,2325-0399
DOI: 10.18576/amis/100125