On the computation of nonhyperbolic fixed points. (English) Zbl 1162.37316

Summary: 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.


37E05 Dynamical systems involving maps of the interval
37M99 Approximation methods and numerical treatment of dynamical systems
39B12 Iteration theory, iterative and composite equations
65J15 Numerical solutions to equations with nonlinear operators


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