5 papers
The Complex Green's Function for Symmetric Sets
Klaus Schiefermayr, Olivier Sète
The aim of this paper is threefold: (i) We study the complex Green's function (the analytic extension of the real Green's function) for multiply connected domains with some symmetr…
On the zeros of polyanalytic polynomials
Olivier Sète, Jan Zur
We give sufficient conditions under which a polyanalytic polynomial of degree has (i) at least one zero, and (ii) finitely many zeros. In the latter case, we prove that the num…
Walsh's Conformal Map onto Lemniscatic Domains for Several Intervals
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the complement of a compact set with components onto a lemniscatic domain …
The first five years of the AAA algorithm
Yuji Nakatsukasa, Olivier Sete, Lloyd N. Trefethen
The AAA algorithm, introduced in 2018, computes best or near-best rational approximations to functions or data on subsets of the real line or the complex plane. It is much faster a…
A Newton method for harmonic mappings in the plane
Olivier Sète, Jan Zur
We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation…