Complex Systems

Newton's Method for Quadratics, and Nested Intervals Download PDF

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


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 .