Inverses of Rational Functions

  • Tamás Dózsa Department of Numerical Analysis, Eötvös Loránd University, Budapest, Hungary and Systems and Control Laboratory, SZTAKI, Budapest, Hungary https://orcid.org/0000-0003-0919-4385
Keywords: rational functions, Blaschke-products, fixed point iterations, winding numbers

Abstract

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.

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Published
2022-10-28
How to Cite
Dózsa, T. (2022). Inverses of Rational Functions. Acta Cybernetica, 26(1), 53-69. https://doi.org/10.14232/actacyb.294975
Section
Special Issue of SCAN 2020