Paper Info
Title
A Family Of Newton-Type Iterative Methods Using Some Special Self-Accelerating Parameters
Abstract
In this paper, a family of Newton-type iterative methods with memory is obtained for solving nonlinear equations, which uses some special self-accelerating parameters. To this end, we first present two optimal fourth-order iterative methods with memory for solving nonlinear equations. Then we give a novel way to construct the self-accelerating parameter and obtain a family of Newton-type iterative methods with memory. The self-accelerating parameters have the properties of simple structure and easy calculation, which do not increase the computational cost of the iterative methods. The convergence order of the new iterative method is increased from 4 to 2 + root 7 approximate to 4.64575. Numerical comparisons are made with some known methods by using the basins of attraction and through numerical computations to demonstrate the efficiency and the performance of the new methods. Experiment results show that, compared with the existing methods, the new iterative methods with memory have the advantage of costing less computing time.
Year
DOI
Venue
2018
10.1080/00207160.2017.1366459
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Keywords
Field
DocType
Iterative method with memory, self-accelerating parameter, root-finding, Newton method, convergence order
Mathematical optimization,Nonlinear system,Iterative method,Relaxation (iterative method),Root-finding algorithm,Local convergence,Mathematics,Matrix-free methods,Newton's method
Journal
Volume
Issue
ISSN
95
10
0020-7160
Citations 
PageRank 
References 
0
0.34
13
Authors
1
Name
Order
Citations
PageRank
Xiaofeng Wang1410.54