Related papers: Multivariate Rational Approximation
We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…
A mathematical model of Subject behaviour choice is proposed. The background of the model is the concept of two preference relations determining Subject behaviour. These are an "internal" or subjective preference relation and an "external"…
The Analytic Hierarchy Process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche introduced a max-algebraic approach to the single criterion AHP. We extend this to the multi-criteria AHP, by…
We strengthen the classical approximation theorems of Weierstrass, Runge and Mergelyan by showing the polynomial and rational approximants can be taken to have a simple geometric structure. In particular, when approximating a function $f$…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
The article proposes a heuristic approximation approach to the bin packing problem under multiple objectives. In addition to the traditional objective of minimizing the number of bins, the heterogeneousness of the elements in each bin is…
Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…
In this paper, we estimate the simultaneous approximation exponents of the values of certain Mahler functions. For this we construct Hermite-Pad\'{e} approximations of the functions under consideration, then apply the functional equations…
Failure probability evaluation for complex physical and engineering systems governed by partial differential equations (PDEs) are computationally intensive, especially when high-dimensional random parameters are involved. Since standard…
We compute the constant of approximation for an arbitrary rational point on an arbitrary smooth cubic hypersurface $X$ over a number field $k$, provided that there is a $k$-rational line somewhere on $X$. In the process, we verify the Coba…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of…
The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the H\"older spaces $H_p^{r,\alpha}$ for all $0<p\le\infty$ and $0<\alpha\le r$. By using modifications of the classical moduli of…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is fundamental to the study and simulation of fractional differential and integral equations. However, these functions are computationally expensive and their numerical…
We exploit the idea to use the maximal-entropy method, successfully tested in information theory and statistical thermodynamics, to determine approximating function's coefficients and squared errors' weights simultaneously as output of one…
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…
This works handles the inverse reinforcement learning problem in high-dimensional state spaces, which relies on an efficient solution of model-based high-dimensional reinforcement learning problems. To solve the computationally expensive…
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…
Here we study theoretically and compare experimentally an efficient method for solving systems of algebraic equations, where the matrix comes from the discretization of a fractional diffusion operator. More specifically, we focus on…