Related papers: Weighted polynomial approximation of rational B\'e…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
We describe a method for computing the highest degree coefficients of a weighted Ehrhart quasi-polynomial for a rational simple polytope.
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…
The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
We propose and study a class of novel algorithms that aim at solving bilinear and quadratic inverse problems. Using a convex relaxation based on tensorial lifting, and applying first-order proximal algorithms, these problems could be solved…
We consider polynomial approximation over the interval $[-1,1]$ by regularized weighted discrete least squares methods with $\ell_2-$ or $\ell_1-$regularization, respectively. As the set of nodes we use Gauss quadrature points (which are…
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 present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
We calculate the Jacobi Eisenstein series of weight $k \ge 3$ for a certain representation of the Jacobi group, and evaluate these at $z = 0$ to give coefficient formulas for a family of modular forms $Q_{k,m,\beta}$ of weight $k \ge 5/2$…
In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…
We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We…
The problem of computing a representation for a real polynomial as a sum of minimum number of squares of polynomials can be casted as finding a symmetric positive semidefinite real matrix (Gram matrix) of minimum rank subject to linear…
We propose a slight modification of the Berlekamp-Massey Algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence. Such a modification enables to explain it in a simpler way and to adapt it to lazy evaluation.
We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…
Partitioning a connected graph into $k$~vertex-disjoint connected subgraphs of similar (or given) orders is a classical problem that has been intensively investigated since late seventies. Given a connected graph $G=(V,E)$ and a weight…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of…
We give a deterministic method of quasi-polynomial complexity to approximate the volume of the intersection of the unit hypercube with two specific sets. The method can actually be applied (without losing the quasi-polynomial complexity) to…