相关论文: On the relation of truncation and approximation er…

Rigorous assessment of uncertainty is crucial to the utility of DNS results. Uncertainties in the computed statistics arise from two sources: finite statistical sampling and the discretization of the Navier-Stokes equations. Due to the…

Finite difference approximation, in addition to Taylor truncation errors, introduces numerical dispersion-and-dissipation errors into numerical solutions of partial differential equations. We analyze a class of finite difference schemes…

This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…

The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…

We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…

We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…

Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…

The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…

The harmonizable Piranashvili-type stochastic processes are approximated by finite time shifted average sampling sums. Explicit truncation error upper bounds are established. Various corollaries and special cases are discussed.

Recently, considerable efforts have been devoted to approximately computing the global and local (i.e., incident to each node) triangle counts of a large graph stream represented as a sequence of edges. Existing approximate triangle…

We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on…

This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…

We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…

This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in…

We present an $rp$-adaptation strategy for high-fidelity simulation of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimiser to $r$-adapt the mesh and…

In finite element methods (FEMs), the accuracy of the solution cannot increase indefinitely because the round-off error increases when the number of degrees of freedom (DoFs) is large enough. This means that the accuracy that can be reached…

Wavelet coefficients are estimated recursively at progressively coarser scales recursively. As a result, the estimation is prone to multiplicative propagation of truncation errors due to quantization and round-off at each stage. Yet, the…

Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…