Inverses of Rational Functions

  • Tamás Dózsa Department of Numerical Analysis, Eötvös Loránd University, Budapest, Hungary and Systems and Control Laboratory, SZTAKI, Budapest, Hungary
Keywords: rational functions, Blaschke-products, fixed point iterations, winding numbers


We consider the numerical construction of inverses for a class of rational functions. We propose two inverse algorithms, which can be used to simultaneously identify every zero of a rational function or polynomial. In the first case, we propose a generalization of an inverse algorithm based on our previous work and specify a class of rational functions, for which this generalized algorithm is applicable. In the second case, we provide a method to construct Blaschke-products, whose roots match the roots of a polynomial or a rational function. We also consider different iterative methods to numerically calculate the inverse points and discuss their properties.


Download data is not yet available.
How to Cite
Dózsa, T. (2022). Inverses of Rational Functions. Acta Cybernetica, 26(1), 53-69.
Special Issue of SCAN 2020