Related papers: suboptimal error estimates for homogenization of l…
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
In this paper, we consider several possible ways to set up Heterogeneous Multiscale Methods for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, which can be seen as a means to modeling rapidly varying…
We prove optimal quantitative estimates on the first-order correctors on supercritical percolation clusters: we show that they are bounded in $d\geq 3$ and have logarithmic growth in $d = 2$, in the sense of stretched exponential moments.…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…
The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schr\"{o}dinger equation at low regularity. Its temporal convergence was recently analyzed in a framework of discrete…
We study the non-parametric estimation of the value ${\theta}(f )$ of a linear functional evaluated at an unknown density function f with support on $R_+$ based on an i.i.d. sample with multiplicative measurement errors. The proposed…
Estimation of a regression function from independent and identically distributed random variables is considered. The $L_2$ error with integration with respect to the design measure is used as an error criterion. Over-parametrized deep…
In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…
In this paper we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently…
In this paper we provide a priori error estimates in standard Sobolev (semi-)norms for approximation in spline spaces of maximal smoothness on arbitrary grids. The error estimates are expressed in terms of a power of the maximal grid…
This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG…
We consider the $L_t^2L_x^r$ estimates for the solutions to the wave and Schr\"odinger equations in high dimensions. For the homogeneous estimates, we show $L_t^2L_x^\infty$ estimates fail at the critical regularity in high dimensions by…
We present the attempt to study the problem of the estimates of higher-order perturbative corrections to physical quantities in the Euclidean region. Our considerations are based on the application of the scheme-invariant methods, namely…
This paper applies a discontinuous Galerkin finite element method to the Kelvin-Voigt viscoelastic fluid motion equations when the forcing function is in $L^\infty({\bf L}^2)$-space. Optimal a priori error estimates in $L^\infty({\bf…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…