相关论文: Caratheodory-Tchakaloff Subsampling

Using the concept of Geometric Weakly Admissible Meshes together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete multivariate least squares approximation and Lagrange…

Many science and engineering applications involve solving a linear least-squares system formed from some field measurements. In the distributed cyber-physical systems (CPS), often each sensor node used for measurement only knows partial…

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…

In this paper, we propose a new approach to justify a round-off error impact on the accuracy of the linear least squares (LS) solution using Cholesky decomposition. This decomposition is widely employed to inverse a matrix in the linear…

We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…

We propose "LEAPS", an algorithm to sample from discrete distributions known up to normalization by learning a rate matrix of a continuous-time Markov chain (CTMC). LEAPS can be seen as a continuous-time formulation of annealed importance…

In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…

This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an…

We study weighted Chebyshev polynomials on compact subsets of the complex plane with respect to a bounded weight function. We establish existence and uniqueness of weighted Chebyshev polynomials and derive weighted analogs of Kolmogorov's…

Compressed manifold modes are locally supported analogues of eigenfunctions of the Laplace-Beltrami operator of a manifold. In this paper we describe an algorithm for the calculation of modes for discrete manifolds that, in experiments,…

Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods…

The Kantorovich-Rubinshtein metric is an $L^1$-like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in…

The Catani--Seymour dipole subtraction is a general and powerful procedure to calculate the QCD next-to-leading order corrections for collider observables. We clearly define a practical algorithm to use the dipole subtraction. The algorithm…

We consider iterative (`turbo') algorithms for compressed sensing. First, a unified exposition of the different approaches available in the literature is given, thereby enlightening the general principles and main differences. In particular…

We prove pseudocompactness of a Tychonoff space $X$ and the space $\mathcal{P}(X)$ of Radon probability measures on it with the weak topology under the condition that the Stone-\v{C}ech compactification of the space $\mathcal{P}(X)$ is…

We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…

Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fr\'echet derivative. In this work, we propose a novel…

We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…

Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…

Non-parametric estimation of a convex discrete distribution may be of interest in several applications, such as the estimation of species abundance distribution in ecology. In this paper we study the least squares estimator of a discrete…