Biological systems can process information without expending energy, and the limit to what can be achieved in this way is known as a Hopfield barrier. We characterize this barrier for the sharpness of ...

Extending a result of Khavinson and $\acute{S}wi\cedil{a}tek$ (2003) we show that the rational harmonic function $\overline {r(z)} - z$, where r(z) is a rational function of degree n > 1, has no more ...

This repository contains benchmarks to compare different algorithms for rational function reconstruction implemented in rare. See data/Readme.md for more information on the sample rational functions.

Abstract: The so-called non-linear vector fitting (NL-VF) technique was recently introduced as a new method for rational function approximation in the frequency domain (FD). While the classical vector ...

For a rational matrix function Φ with poles outside the unit circle, we estimate the degree of the unique superoptimal approximation 𝒜Φ by matrix functions analytic in the unit disk. We obtain sharp ...