A new iterative method for the computation of the solutions of nonlinear equations

被引:12
作者
Costabile, F [1 ]
Gualtieri, MI [1 ]
Luceri, R [1 ]
机构
[1] UNICAL, Dept Math, I-87036 Arcavacata Di Rende, Cs, Italy
关键词
Assure; Iterative Method; Nonlinear Equation; Newton Method; Numerical Test;
D O I
10.1023/A:1014078328575
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Recently, by Costabile, Gualtieri and Serra (1999), an iterative method was presented for the computation of zeros of C-1 functions. This method combines the assured convergence of the bisection-like algorithms with a superlinear convergence speed which characterizes Newton-like methods. The order of the method and the cost per iteration is exactly equivalent to the Newton method. In this paper we present a new iterative method for the computation of the zeros of C-1 functions with the same properties of convergence as the method proposed by Costabile, Gualtieri and Serra (1999) but with order 1 + root2 = 2.41 for C-3 functions. Compared with the methods of order 1 + root2 presented by Traub ( 1964), our methods ensure Global convergence. Then we consider a generalization of this procedure which gives a class of methods of order (n + rootn(2) + 4)/2, where n is the degree of the approximating polynomial, with one-point iteration functions with memory. Finally a number of numerical tests are performed. The numerical results seem to show that, at least on a set of problems, the new methods work better than the methods proposed, and, therefore, than both the Newton and Alefeld and Potra (1992) methods.
引用
收藏
页码:87 / 100
页数:14
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