RECURRENCE RELATIONS FOR RATIONAL CUBIC METHODS .1. THE HALLEY METHOD

被引：150
|
作者：
CANDELA, V
MARQUINA, A
机构：
[1] Departmento de Análisis Matemático, University of Valencia, Burjassot (Valencia), 46100, C/Dr. Moliner
来源：
COMPUTING | 1990年 / 44卷 / 02期
关键词：
a priori error bounds; AMS Subject Classification (1980): Primary: 65J15; non-linear equations; Third order iterative methods;
D O I：
10.1007/BF02241866
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper we present a system of a priori error bounds for the Halley method in Banach spaces. Our theorem supplies sufficient conditions on the initial point to ensure the convergence of Halley iterates, by means of a system of "recurrence relations", analogous to those given for the Newton method by Kantorovich, improving previous results by Döring [4]. The error bounds presented are optimal for second degree polynomials. Other rational cubic methods, as the Chebyshev method, will be treated in a subsequent paper. © 1990 Springer-Verlag.
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页码：169 / 184
页数：16
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