相关论文: Enhanced Error Estimates for Augmented Subspace Me…

In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…

The Crouzeix--Raviart finite element method is widely recognized in the field of finite element analysis due to its nonconforming nature. The main goal of this paper is to present a general strategy for enhancing the Crouzeix--Raviart…

We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…

Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…

Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of…

There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…

This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…

The cubic regularization (CR) algorithm has attracted a lot of attentions in the literature in recent years. We propose a new reformulation of the cubic regularization subproblem. The reformulation is an unconstrained convex problem that…

This paper is to give a new understanding and applications of the subspace projection method for selfadjoint eigenvalue problems. A new error estimate in the energy norm, which is induced by the stiff matrix, of the subspace projection…

The subspace-based techniques are widely utilized in various scientific fields, and they need accurate estimation of the signal subspace dimension. The classic RMT estimator for model order estimation based on random matrix theory assumes…

Previous methods decompose the blind super-resolution (SR) problem into two sequential steps: \textit{i}) estimating the blur kernel from given low-resolution (LR) image and \textit{ii}) restoring the SR image based on the estimated kernel.…

A two-grid scheme based on mixed finite-element approximations to the incompressible Navier-Stokes equations is introduced and analyzed. In the first level the standard mixed finite-element approximation over a coarse mesh is computed. In…

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…

We verify quasi-optimality of the Crouzeix-Raviart FEM for nonlinear problems of $p$-Laplace type. More precisely, we show that the error of the Crouzeix-Raviart FEM with respect to a quasi-norm is bounded from above by a uniformly bounded…

In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a $(p,\delta)$-structure for some $p\in (1,\infty)$ and $\delta\ge 0$. We establish a priori error estimates, which are…

A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…

We address the problem of structured covariance matrix estimation for radar space-time adaptive processing (STAP). A priori knowledge of the interference environment has been exploited in many previous works to enable accurate estimators…

This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs…

This paper presents novel methods for estimating certified radii in randomized smoothing, a technique crucial for certifying the robustness of neural networks against adversarial perturbations. Our proposed techniques significantly improve…

We investigate the piecewise linear nonconforming Crouzeix-Raviar and the lowest order Raviart-Thomas finite-element methods for the Poisson problem on three-dimensional anisotropic meshes. We first give error estimates of the…