Related papers: Multivariate approximation of functions on irregul…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…

We consider the problem of approximating a function in general nonlinear subsets of $L^2$ when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…

In this work, we construct a stable and fairly fast estimator for solving non-parametric multidimensional regression problems. The proposed estimator is based on the use of multivariate Jacobi polynomials that generate a basis for a reduced…

A common way to estimate an unknown convex regression function $f_0: \Omega \subset \mathbb{R}^d \rightarrow \mathbb{R}$ from a set of $n$ noisy observations is to fit a convex function that minimizes the sum of squared errors. However,…

We present a methodology to investigate phase-diagrams of quantum models based on the principle of the reduced basis method (RBM). The RBM is built from a few ground-state snapshots, i.e., lowest eigenvectors of the full system Hamiltonian…

In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…

Variational quantum algorithms are a class of techniques intended to be used on near-term quantum computers. The goal of these algorithms is to perform large quantum computations by breaking the problem down into a large number of shallow…

Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_2$ on a usual compact space $\mathcal M$, Gr\"ochenig introduced the weighted least squares polynomials and the least squares quadrature from pointwise samples of a function, and…

In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required…

This paper proposes a distributed weighted regularized least squares algorithm (DWRLS) based on spherical radial basis functions and spherical quadrature rules to tackle spherical data that are stored across numerous local servers and…

We present the new Orthogonal Polynomials Approximation Algorithm (OPAA), a parallelizable algorithm that estimates probability distributions using functional analytic approach: first, it finds a smooth functional estimate of the…

We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes…

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…

We study orthogonal polynomials on a fully symmetric planar domain $\Omega$ that is generated by a certain triangle in the first quadrant. For a family of weight functions on $\Omega$, we show that orthogonal polynomials that are even in…

We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…

This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal…

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…