Related papers: Chebyshev approximation of exponential data
In this paper, we discuss asymptotic relations for the approximation of $\left\vert x\right\vert ^{\alpha},\alpha>0$ in $L_{\infty}\left[ -1,1\right] $ by Lagrange interpolation polynomials based on the zeros of the Chebyshev polynomials of…
We establish a new extremal property of the classical Chebyshev polynomials in the context of best rank-one approximation of tensors. We also give some necessary conditions for a tensor to be a minimizer of the ratio of spectral and…
We prove in this paper that the expected value of the objective function of the $k$-means++ algorithm for samples converges to population expected value. As $k$-means++, for samples, provides with constant factor approximation for $k$-means…
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…
The error term in the approximate functional equation for exponential sums involving the divisor function will be improved under certain conditions for the parameters of the approximate functional equation.
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…
This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…
This paper establishes the nearly optimal rate of approximation for deep neural networks (DNNs) when applied to Korobov functions, effectively overcoming the curse of dimensionality. The approximation results presented in this paper are…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
In the empirical study of evolutionary algorithms, the solution quality is evaluated by either the fitness value or approximation error. The latter measures the fitness difference between an approximation solution and the optimal solution.…
We investigate the convergence properties of the EM algorithm when applied to overspecified Gaussian mixture models -- that is, when the number of components in the fitted model exceeds that of the true underlying distribution. Focusing on…
We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…
To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…
We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.
We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than…
We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found.…
In the domain of physics experiments, data fitting is a pivotal technique for extracting insights from both experimental and simulated datasets. This article presents an approximation method designed to estimate the systematic errors…
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…
In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for…