Related papers: Tent-transformed lattice rules for integration and…
This paper is concerned with quadrature/cubature rules able to deal with multiple subspaces of functions, in such a way that the integration points are common for all the subspaces, yet the weights are tailored to each specific subspace.…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
Our main interest in this paper is to study some approximation problems for classes of functions with mixed smoothness. We use technique, based on a combination of results from hyperbolic cross approximation, which were obtained in 1980s --…
In the present paper we study quasi-Monte Carlo rules for approximating integrals over the $d$-dimensional unit cube for functions from weighted Sobolev spaces of regularity one. While the properties of these rules are well understood for…
Consider the numerical integration $${\rm Int}_{\mathbb S^d,w}(f)=\int_{\mathbb S^d}f({\bf x})w({\bf x}){\rm d}\sigma({\bf x}) $$ for weighted Sobolev classes $BW_{p,w}^r(\mathbb S^d)$ with a Dunkl weight $w$ and weighted Besov classes…
Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…
Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-$1$ lattice rule to approximate an $s$-dimensional integral is fully specified by its \emph{generating vector}…
We prove upper bounds on the order of convergence of Frolov's cubature formula for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundary condition. More precisely, we study…
In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…
We propose a method to obtain the optimal weight function of 9 paths in (3+1)D space-time whose length is less than or equal to $2\times (6+2)$ lattice units. The factor 2 comes from inclusion of opposite direction path or time reversed…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
In the numerical linear algebra community, it was suggested that to obtain nearly optimal bounds for various problems such as rank computation, finding a maximal linearly independent subset of columns (a basis), regression, or low-rank…
We study integration and $L^2$-approximation of functions of infinitely many variables in the following setting: The underlying function space is the countably infinite tensor product of univariate Hermite spaces and the probability measure…
In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions. The invariance is either by translations under a…
Randomized quadratures for integrating functions in Sobolev spaces of order $\alpha \ge 1$, where the integrability condition is with respect to the Gaussian measure, are considered. In this function space, the optimal rate for the…