zbMATH — the first resource for mathematics

Möbius splines are closed under continuous iteration. (English) Zbl 1017.65104
The paper is devoted to explicit computational procedures for exactly computing the fractional iterates of a Möbius spline, i.e. a function that is monotonic, continuously differentiable and is piecewise homographic transformation. It is shown that the fractional iterate of a Möbius spline is itself a Möbius spline. A simple algorithm for computing composition and fractional iterates is suggested. There is some discussion of applying Möbius splines in numerical solution of functional equations.

65Q05 Numerical methods for functional equations (MSC2000)
39B12 Iteration theory, iterative and composite equations
Full Text: DOI