On Newton's method applied to real polynomials

Abstract

It is known that if we apply Newton's method to the complex function , with , 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 , then there is at least one immediate basin of attraction having infinite area.

Keywords:

• Newton's method
• basin of attraction
• rational iteration

Acknowledgements

The second author is partially supported by the Catalan grant 2009SGR-792, by the Spanish grants MTM-2008-01486 and MTM-2006-05849 Consolider (including a FEDER contribution), and by the European network 035651-2-CODY.