On Newton's method applied to real polynomials

被引：1
|
作者：
Cilingir, Figen [2 ]
Jarque, Xavier [1 ]
机构：
[1] Univ Rovira & Virgili, Dept Engn Informat & Matemat, Tarragona 43007, Spain
[2] Cankaya Univ, Dept Math & Comp, Ankara, Turkey
来源：
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2012年 / 18卷 / 06期
关键词：
Newton's method; basin of attraction; rational iteration; COMPLEX EXPONENTIAL FUNCTION; AREA;
D O I：
10.1080/10236198.2010.547493
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is known that if we apply Newton's method to the complex function F(z) = P(z)e(Q(z)), with deg(Q) > 2, then the immediate basin of attraction of the roots of P has finite area. In this paper, we show that under certain conditions on the polynomial P, if deg(Q) = 1, then there is at least one immediate basin of attraction having infinite area.
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页码：1067 / 1076
页数：10
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