Related papers: Rational approximation of the absolute value funct…
This work brings together the moment matching approach based on Loewner functions and the classical Loewner framework based on the Loewner pencil in the case of bilinear systems. New Loewner functions are defined based on the bilinear…
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some linear methods of this approximation for univariate functions in the class induced by the convolution…
We establish a quantitative approximation formula of the Lyapunov exponent of a rational function of degree more than one over an algebraically closed field of characteristic $0$ that is complete with respect to a non-trivial and possibly…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Methods have previously been developed for the approximation of Lyapunov functions using radial basis functions. However these methods assume that the evolution equations are known. We consider the problem of approximating a given Lyapunov…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
In scientific computing, the acceleration of atomistic computer simulations by means of custom hardware is finding ever growing application. A major limitation, however, is that the high efficiency in terms of performance and low power…
This paper is concerned with minimizing a sum of rational functions over a compact set of high-dimension. Our approach relies on the second Lasserre's hierarchy (also known as the upper bounds hierarchy) formulated on the pushforward…
We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal…
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…
In this paper, we continue to study properties of rational approximations to Euler's constant and values of the Gamma function defined by linear recurrences, which were found recently by A. I. Aptekarev and T. Rivoal. Using multiple…
We present new convolution based smooth approximations to the absolute value function and apply them to construct gradient based algorithms such as the nonlinear conjugate gradient scheme to obtain sparse, regularized solutions of linear…
We propose a novel value function approximation technique for Markov decision processes. We consider the problem of compactly representing the state-action value function using a low-rank and sparse matrix model. The problem is to decompose…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…
We consider in this paper the optimal approximations of convex univariate functions with feed-forward Relu neural networks. We are interested in the following question: what is the minimal approximation error given the number of…
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new…
The papers shows an algorithm to search for approximations of reals to rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.
Vector Fitting (VF) is a popular method of constructing rational approximants that provides a least squares fit to frequency response measurements. In an earlier work, we provided an analysis of VF for scalar-valued rational functions and…