相关论文: The effects of rounding errors in the nodes on bar…

This work derives a posteriori error estimate of polygonal finite element methods based on Wachspress barycentric coordinates. In particular, we prove that the classical residual-based a posteriori error estimator is both an upper and lower…

Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…

This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an…

Some new rigorous perturbation bounds for the generalized Cholesky factorization with normwise or componentwise perturbations in the given matrix are obtained, where the componentwise perturbation has the form of backward rounding error for…

The one-loop NLO radiative corrections to the observables in polarized DIS using assumption that a quark is an essential massive particle are considered. If compared with classical QCD formulae the obtained results are identical for the…

The goal of this work is to introduce a local and a global interpolator in Jacobi-weighted spaces, with optimal order of approximation in the context of the $p$-version of finite element methods. Then, an a posteriori error indicator of the…

A systematic investigation of the nuclear-polarization effects in one- and few-electron heavy ions is presented. The nuclear-polarization corrections in the zeroth and first orders in $1/Z$ are evaluated to the binding energies, the…

In this paper, we study the optimal general convergence rates for quadratures derived from Chebyshev points. By building on the aliasing errors on integration of Chebyshev polynomials, together with the asymptotic formulae on the…

We compute the equilibrium concentration of stacking faults and point defects in polydisperse hard-sphere crystals. We find that, while the concentration of stacking faults remains similar to that of monodisperse hard sphere crystals, the…

We evaluate the impact of electroweak corrections of infrared origin on longitudinal strongly interacting gauge bosons scattering, calculating all order resummed expressions at the double log level. As a working example, we consider the…

We study the influence of an imperfect structure of a crystalline undulator on the spectrum of the undulator radiation. The main attention is paid to the undulators in which the periodic bending in the bulk appears as a result of a regular…

We broadly explore the effects of systematic errors on reverberation mapping lag uncertainty estimates from {\tt JAVELIN} and the interpolated cross-correlation function (ICCF) method. We focus on simulated lightcurves from random…

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…

Forthcoming large-scale surveys will soon attempt to measure cosmic shear to an unprecedented level of accuracy, requiring a similarly high level of accuracy in the shear measurements of galaxies. Factors such as pixelisation, imperfect…

This article deals with error estimates for the finite element approximation of variational normal derivatives and, as a consequence, error estimates for the finite element approximation of Dirichlet boundary control problems with energy…

The presence of interference, where the outcome of an individual may depend on the treatment assignment and behavior of neighboring nodes, can lead to biased causal effect estimation. Current approaches to network experiment design focus on…

In very crowded fields, the modulation of the background by the sea of unresolved faint sources induces centroid shifts. The errors increase with the number of sources per beam. Even the most optimistic simulations of imaging data show that…

The aim of this paper is to give a short overview on error bounds and to provide the first bricks of a unified theory. Inspired by the works of [8, 15, 13, 16, 10], we show indeed the centrality of the Lojasiewicz gradient inequality. For…

Next generation radio telescope arrays are being designed and commissioned to accurately measure polarized intensity and rotation measures across the entire sky through deep, wide-field radio interferometric surveys. Radio interferometer…

Common model selection criteria, such as $AIC$ and its variants, are based on in-sample prediction error estimators. However, in many applications involving predicting at interpolation and extrapolation points, in-sample error cannot be…