Related papers: Rigorous a-posteriori analysis using numerical eig…
Soft error rates are increasing as modern architectures require increasingly small features at low voltages. Due to the large number of components used in HPC architectures, these are particularly vulnerable to soft errors. Hence, when…
Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…
We establish sharp global rigidity upper bounds for universal determinantal point processes describing edge eigenvalues of random matrices. For this, we first obtain a general result which can be applied to general (not necessarily…
As datasets used in scientific applications become more complex, studying the geometry and topology of data has become an increasingly prevalent part of the data analysis process. This can be seen for example with the growing interest in…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete…
We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a "post-processing algorithm", checking that…
A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator…
In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the…
Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper…
We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
We asymptotically estimate from above the expected Betti numbers of random real hypersurfaces in smooth real projective manifolds. Our upper bounds grow as the square root of the degree of the hypersurfaces as the latter grows to infinity,…
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are…
This work concerns the numerical analysis of the linear elasticity problem with a Robin boundary condition on a smooth domain. A finite element discretization is presented using high-order curved meshes in order to accurately discretize the…
This paper is devoted to order-one explicit approximations of random periodic solutions to multiplicative noise driven stochastic differential equations (SDEs) with non-globally Lipschitz coefficients. The existence of the random periodic…
For each $n$, let RD$(n)$ denote the minimum $d$ for which there exists a formula for the general polynomial of degree $n$ in algebraic functions of at most $d$ variables. In this paper, we recover an algorithm of Sylvester for determining…
In this paper, based on the combination of tensor neural network and a posteriori error estimator, a novel type of machine learning method is proposed to solve high-dimensional boundary value problems with homogeneous and non-homogeneous…