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.
"On the Computation of Nonhyperbolic Fixed Points." Experiment. Math. 11 (4) 477 - 485, 2002.