Related papers: ZERNIPAX: A Fast and Accurate Zernike Polynomial C…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
We present an overview of Sherpa, an open source Python project, and discuss its development history, broad design concepts and capabilities. Sherpa contains powerful tools for combining parametric models into complex expressions that can…
Optical multilayer thin-films are fundamental components that enable the precise control of reflectance, transmittance, and phase shift in the design of photonic systems. Rapid and accessible simulation of these structures holds critical…
Wavefront reconstruction is a critical component in various optical systems, including adaptive optics, interferometry, and phase contrast imaging. Traditional reconstruction methods often employ either the Cartesian (pixel) basis or the…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
We design an algorithm to compute the Newton polytope of the resultant, known as resultant polytope, or its orthogonal projection along a given direction. The resultant is fundamental in algebraic elimination, optimization, and geometric…
In this work we introduce a new polynomial representation of the Bernoulli numbers in terms of polynomial sums allowing on the one hand a more detailed understanding of their mathematical structure and on the other hand provides a…
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…
Let $d\nu$ be a measure in $\mathbb{R}^d$ obtained from adding a set of mass points to another measure $d\mu$. Orthogonal polynomials in several variables associated with $d\nu$ can be explicitly expressed in terms of orthogonal polynomials…
In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving…
A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented.
We study the structure of the zeros of optimal polynomial approximants to reciprocals of functions in Hilbert spaces of analytic functions in the unit disk. In many instances, we find the minimum possible modulus of occurring zeros via a…
OGRePy is a modern, open-source Python package designed to perform symbolic tensor calculations, with a particular focus on applications in general relativity. Built on an object-oriented architecture, OGRePy encapsulates tensors, metrics,…
Accurate simulations of combustion phenomena require the use of detailed chemical kinetics in order to capture limit phenomena such as ignition and extinction as well as predict pollutant formation. However, the chemical kinetic models for…
Zernike polynomials are one of the most widely used mathematical descriptors of optical aberrations in the fields of imaging and adaptive optics. Their mathematical orthogonality as well as isomorphisms with experimentally observable…
Given a function from $\mathbb{Z}_n$ to itself one can determine its polynomial representability by using Kempner function. In this paper we present an alternative characterization of polynomial functions over $\mathbb{Z}_n$ by constructing…
KerrGeoPy is a Python package which computes both stable and plunging timelike geodesics in Kerr spacetime using analytic solutions to the geodesic equation that are written in terms of Legendre elliptic integrals. It mirrors and builds…
Pyserini is an easy-to-use Python toolkit that supports replicable IR research by providing effective first-stage retrieval in a multi-stage ranking architecture. Our toolkit is self-contained as a standard Python package and comes with…
This study presents the derivation of a recursive formula for integrals of products of $N$ Hermite polynomials, establishing a numerically stable scheme for their accurate evaluation in computer codes. The derivation is notably simple and…
We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with point masses…