Related papers: Truncation Dimension for Function Approximation
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…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In truncated partial-wave analysis, one fits observables that are bilinear in the amplitudes rather than the amplitudes themselves. Truncation is therefore not merely a restriction of the amplitude basis, but of the bilinear interference…
Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
We consider approximations of a continuous function on a countable normed Fr\'{e}chet space by analytic and $*$-analytic. Also we found a criterium of the existence of an extension of a continuous function from a dense subspace of a…
The problem of estimating, from a random sample of points, the dimension of a compact subset $S$ of the Euclidean space is considered. The emphasis is put on consistency results in the statistical sense. That is, statements of convergence…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation…
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…
The solution to Poisson's equation arise in many Markov chain and Markov jump process settings, including that of the central limit theorem, value functions for average reward Markov decision processes, and within the gradient formula for…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
In this manuscript, we provide a concise review of the concept of metric dimension for both deterministic as well as random graphs. Algorithms to approximate this quantity, as well as potential applications, are also reviewed. This work has…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…