A QUADRAPARAMETRIC FAMILY OF EIGHTH-ORDER ROOT-FINDING METHODS
نویسندگان
چکیده
منابع مشابه
A 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.
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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...
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A one parameter family of iteration functions for finding roots is derived. ] h e family includes the Laguerre, Halley, Ostrowski and Euler methods and, as a limiting case, Newton's method. All the methods of the family are cubically convergent for a simple root (except Newton's which is quadratically convergent). The superior behavior of Laguerre's method, when starting from a point z for whic...
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 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...
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ژورنال
عنوان ژورنال: Journal of the Chungcheong Mathematical Society
سال: 2014
ISSN: 1226-3524
DOI: 10.14403/jcms.2014.27.1.133