On Newton’s method applied to real polynomials. (English) Zbl 1243.65048
Summary: 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.
MSC:
| 65H04 | Numerical computation of roots of polynomial equations |
| 65E05 | General theory of numerical methods in complex analysis (potential theory, etc.) |
Keywords:
Newton’s method; basin of attraction; rational iteration; real polynomials; complex functionReferences:
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