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.

引用

页码：1067 / 1076

页数：10

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