Newton's Method for Quadratics, and Nested Intervals
Mordecai J. Golin
Deptartment of Computer Science, Hong Kong UST
Clear Water Bay, Kowloon, Hong Kong
Kenneth J. Supowit
Department of Computer and Information Science,
Ohio State University, Columbus, Ohio 43210, USA
Abstract
The function 
is the Newton map associated with the quadratic polynomial 
. The iterated dynamics of 
on 
is usually studied by exploiting the conjugacy between and the function 
. In this paper we show how to use the technique of nested intervals to yield a direct analysis of the dynamics. We also show how to use the same technique to analyze the dynamics of the function 
.
