401 citations · 571 across the 24 of their papers we have counts for
24 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…
Stochastic Galerkin method and port-Hamiltonian form for linear first-order ordinary differential equations
Roland Pulch, Olivier Sète
We consider linear first-order systems of ordinary differential equations (ODEs) in port-Hamiltonian (pH) form. Physical parameters are remodelled as random variables to conduct an…
Walsh's Conformal Map onto Lemniscatic Domains for Polynomial Pre-images II
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the exterior of a set consisting of compact disjoint components onto a lemniscatic domain. In particular, w…
The Helmholtz equation with uncertainties in the wavenumber
Roland Pulch, Olivier Sète
We investigate the Helmholtz equation with suitable boundary conditions and uncertainties in the wavenumber. Thus the wavenumber is modeled as a random variable or a random field.…
Walsh's conformal map onto lemniscatic domains for polynomial pre-images I
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the exterior of a compact set onto a lemniscatic domain. If is simply connected, the lemniscatic domain is the e…
Computing the logarithmic capacity of compact sets having (infinitely) many components with the Charge Simulation Method
Jörg Liesen, Mohamed M. S. Nasser, Olivier Sète
We apply the Charge Simulation Method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many "small" components. This application allows…
The transport of images method: computing all zeros of harmonic mappings by continuation
Olivier Sète, Jan Zur
We present a continuation method to compute all zeros of a harmonic mapping in the complex plane. Our method works without any prior knowledge of the number of zeros or their a…
Minimal degree rational open up mappings and related questions
Sergei Kalmykov, Béla Nagy, Olivier Sète
We establish the existence and uniqueness of rational conformal maps of minimal degree for opening up arcs. In earlier results, the degree was exponential in . We also…
Number and location of pre-images under harmonic mappings in the plane
Olivier Sète, Jan Zur
We derive a formula for the number of pre-images under a non-degenerate harmonic mapping , using the argument principle. This formula reveals a connection between the pre-images…
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…
The index of singular zeros of harmonic mappings of anti-analytic degree one
Robert Luce, Olivier Sète
We study harmonic mappings of the form , where is an analytic function. In particular we are interested in the index (a generalized multiplicity) of…
The AAA algorithm for rational approximation
Yuji Nakatsukasa, Olivier Sète, Lloyd N. Trefethen
We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of Matlab and requiring no user input parameters.…
Fast and accurate computation of the logarithmic capacity of compact sets
Jörg Liesen, Olivier Sète, Mohamed M. S. Nasser
We present a numerical method for computing the logarithmic capacity of compact subsets of , which are bounded by Jordan curves and have finitely connected complement.…
Numerical computation of the conformal map onto lemniscatic domains
Mohamed M. S. Nasser, Jörg Liesen, Olivier Sète
We present a numerical method for the computation of the conformal map from unbounded multiply-connected domains onto lemniscatic domains. For -times connected domains the me…
Properties and examples of Faber--Walsh polynomials
Olivier Sète, Jörg Liesen
The Faber--Walsh polynomials are a direct generalization of the (classical) Faber polynomials from simply connected sets to sets with several simply connected components. In this p…
On conformal maps from multiply connected domains onto lemniscatic domains
Olivier Sète, Jörg Liesen
We study conformal maps from multiply connected domains in the extended complex plane onto lemniscatic domains. Walsh proved the existence of such maps in 1956 and thus obtained a…
A Note on the Maximum Number of Zeros of
Robert Luce, Olivier Sète, Jörg Liesen
An important theorem of Khavinson & Neumann (Proc. Amer. Math. Soc. 134(4), 2006) states that the complex harmonic function , where is a rational function of de…
Creating images by adding masses to gravitational point lenses
Olivier Sète, Robert Luce, Jörg Liesen
A well-studied maximal gravitational point lens construction of S. H. Rhie produces images of a light source using deflector masses. The construction arises from a circu…
Perturbing rational harmonic functions by poles
Olivier Sète, Robert Luce, Jörg Liesen
We study how adding certain poles to rational harmonic functions of the form , with rational and of degree , affects the number of zeros of the result…
Sharp parameter bounds for certain maximal point lenses
Robert Luce, Olivier Sète, Jörg Liesen
Starting from an -point circular gravitational lens having images, Rhie (2003) used a perturbation argument to construct an -point lens producing images. In t…
Some properties of Faber-Walsh polynomials
Olivier Sète
Walsh introduced a generalisation of Faber polynomials to certain compact sets which need not be connected. We derive several equivalent representations of these Faber-Walsh polyno…