Higher Order Methods for Nonlinear Equations and Their Basins of Attraction
نویسندگان
چکیده
منابع مشابه
Higher Order Methods for Nonlinear Equations and Their Basins of Attraction
Abstract: In this paper, we have presented a family of fourth order iterative methods, which uses weight functions. This new family requires three function evaluations to get fourth order accuracy. By the Kung–Traub hypothesis this family of methods is optimal and has an efficiency index of 1.587. Furthermore, we have extended one of the methods to sixth and twelfth order methods whose efficien...
متن کاملSome Iterative Methods Free from Derivatives and Their Basins of Attraction for Nonlinear Equations
First, we make the Jain’s derivative-free method optimal and subsequently increase its efficiency index from 1.442 to 1.587. Then, a novel three-step computational family of iterative schemes for solving single variable nonlinear equations is given. The schemes are free from derivative calculation per full iteration. The optimal family is constructed by applying the weight function approach alo...
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There are several third order methods for solving a nonlinear algebraic equation having roots of a givenmultiplicitym. Here we compare a recent family of methods of order three to Euler– Cauchy’s method which is found to be the best in the previous work. There are fewer fourth order methods for multiple roots but we will not include them here. Published by Elsevier Inc.
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 کاملBasins of attraction for several methods to find simple roots of nonlinear equations
There are many methods for solving a nonlinear algebraic equation. The methods are classified by the order, informational efficiency and efficiency index. Here we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss several third and fourth order methods to find simple zeros. The relationship between the basins of attraction and the c...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2016
ISSN: 2227-7390
DOI: 10.3390/math4020022