Related papers: A multivariate generalization of Prony's method
Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an $n$-variate polynomial with bounded individual degree $d$ and…
The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be…
Recovering probability measures from moments is a central theme in statistics and optimization. In particular, we focus on the recovery of measures from moments and pseudo-moments, which may come from solving the moment-SOS hierarchy in one…
Due to its intimate relation to Spectral Theory and Schr\"{o}dinger operators, the multivariate moment problem has been a subject of many researches, so far without essential success (if one compares with the one--dimensional case). In the…
For some kernel matrices, low-rank approximations can be quickly obtained via analytic techniques. One important class of analytic methods that has received attention in recent years is based on the use of proxy points. Accuracy analysis…
Approximate vanishing ideal is a concept from computer algebra that studies the algebraic varieties behind perturbed data points. To capture the nonlinear structure of perturbed points, the introduction of approximation to exact vanishing…
This article investigates parameter estimation of affine term structure models by means of the generalized method of moments. Exact moments of the affine latent process as well as of the yields are obtained by using results derived for…
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…
The aim of the article is to recover a certain type of finite parametric distributions and functions using their spherical mean transform which is given on a certain family of spheres whose centers belong to a finite set $\Gamma$. For this,…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…
Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the Expectation Maximization (EM) algorithm, in which updates…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
We study the recovery of a finitely supported distribution, a complex linear combination of Dirac measures, from intensity measurements. The distribution $\mu=\sum_{j=1}^{s}c_{j}\delta_{t_{j}}$ is given by a coefficient vector…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional…