On the Computation of Nonhyperbolic Fixed Points

Abstract

In order to deal with nonhyperbolic fixed points of a given real iteration function g, we construct new iteration functions C which will be called combined. When a nonhyperbolic fixed point of g becomes a super attractor fixed point of C, the iteration function C is called flat.

Some flat iteration functions are constructed based on Newton's iteration function. Several numerical examples illustrating the good properties of flat iteration functions are presented.

Keywords:

• Fixed point
• nonhyperbolic
• super-attracting fixed point
• iteration function
• order of covergence