Related papers: Physically interpretable approximations of many-bo…
Evaluating the action of a matrix function on a vector, that is $x=f(\mathcal M)v$, is an ubiquitous task in applications. When $\mathcal M$ is large, one usually relies on Krylov projection methods. In this paper, we provide effective…
The spectral function for finite nuclei is computed within the framework of the Local Density Approximation, starting from nuclear matter spectral functions obtained with a realistic nucleon-nucleon interaction. The spectral function is…
Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…
New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the…
The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a…
A Voigt profile function emerges in several physical investigations (e.g. atmospheric radiative transfer, astrophysical spectroscopy, plasma waves and acoustics) and it turns out to be the convolution of the Gaussian and the Lorentzian…
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil $(A,B)$. Based on Zolotarev's best rational function approximations of the signum function and conformal…
Set functions with convenient properties (such as submodularity) appear in application areas of current interest, such as algorithmic game theory, and allow for improved optimization algorithms. It is natural to ask (e.g., in the context of…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were…
Efficient Green's function evaluation in layered media is a holy-grail of wave theory in general and for electromagnetics in particular. While there is a very large amount of knowledge in this context with vast literature, there are yet…
Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or…
In the pursuit of numerically identifying the ground state of quantum many-body systems, approximate quantum wavefunction ansatzes are commonly employed. This study focuses on the spectral decomposition of these approximate quantum…
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the…
For many of the physical phenomena around us, we have developed sophisticated models explaining their behavior. Nevertheless, inferring specifics from visual observations is challenging due to the high number of causally underlying physical…
We investigate methods to calibrate the non-common path aberrations at an adaptive optics system having a wavefront-correcting device working at an extremely high resolution (larger than 150x150). We use focal-plane images collected…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…
In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…
In this paper we study the question of effective field assignment to measured or nonperturbatively calculated spectral functions. The straightforward procedure is to approximate it by a sum of independent Breit-Wigner resonances, and assign…