On the Convergence of Halley's Method for Multiple Polynomial Zeros

被引：16
|
作者：
Proinov, Petko D. [1 ]
Ivanov, Stoil I. [2 ]
机构：
[1] Paisij Hilendarski Univ Plovdiv, Fac Math & Informat, Plovdiv 4000, Bulgaria
[2] Paisij Hilendarski Univ Plovdiv, Fac Phys & Engn Technol, Plovdiv 4000, Bulgaria
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2015年 / 12卷 / 02期
关键词：
Halley's method; polynomial zeros; multiple zeros; local convergence; error estimates; FINDING METHODS; NEWTONS METHOD; ROOTS; FAMILY;
D O I：
10.1007/s00009-014-0400-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the local convergence of Halley's method for the computation of a multiple polynomial zero with known multiplicity. We establish two local convergence theorems for Halley's method for multiple polynomial zeros under different initial conditions. The convergence of these results is cubic right from the first iteration. Also we find an initial condition which guarantees that an initial guess is an approximate zero of the second kind for Halley's method. All of the results are new even in the case of simple zeros.
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页码：555 / 572
页数：18
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