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.

引用

页码：169 / 184

页数：16

共 16 条

[1] ON THE CONVERGENCE OF HALLEYS METHOD [J].