Related papers: A priori error estimates for Lagrange interpolatio…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
Velocity fields with low regularity (below the Lipschitz threshold) naturally arise in many models from mathematical physics, such as the inhomogeneous incompressible Navier-Stokes equations, and play a fundamental role in the analysis of…
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
This paper contains a survey of results obtained by the authors mostly during the past few years and published by 2021. In particular, we present the best of known estimates of numerical characteristics related to the research theme.…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
This paper deals with the error estimate in problems of periodic homogenization. The methods used are those of the periodic unfolding. We give the upper bound of the distance between the unfolded gradient of a function belonging to…
We prove quasi-optimal a priori error estimates for finite element approximations of boundary normal fluxes in the $L^2$-norm. Our results are valid for a variety of different schemes for weakly enforcing Dirichlet boundary conditions…
High-accuracy dimensional measurements by laser interferometers require corrections because of diffraction, which makes the effective fringe-period different from the wavelength of a plane (or spherical) wave $\lambda_0$. By using a…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
We investigate a time-domain Galerkin boundary element method for the wave equation outside a Lipschitz obstacle in an absorbing half-space. A priori estimates are presented for both closed surfaces and screens, and we discuss the relevant…
For a class of parametric modal regression models with measurement error, a simulation extrapolation estimation procedure is proposed in this paper for estimating the modal regression coefficients. Large sample properties of the proposed…
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…
We outline the super-resolution reconstruction problem posed as a maximization of probability. We then introduce an interpolation method based on polygonal pixel overlap, express it as a linear operator, and use it to improve…
We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension $n\geq3$. We prove, by multiplier techniques in the sense of Morawetz, a family of a priori estimates from which the limiting…
We revisit here a fundamental result on planar triangulations, namely that the flip distance between two triangulations is upper-bounded by the number of proper intersections between their straight-segment edges. We provide a complete and…
We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequality first introduced in [6]}) and second inequalities on…
We consider a multivariate piecewise linear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivariate piecewise linear interpolator is…
The paper contains a survey of the results obtained by the author in recent years. These results concern the application in multivariate polynomial interpolation of some geometric constructions and methods. In particular, we give estimates…
The numerical analysis of gradient inclusions in a compact subset of $2\times 2$ diagonal matrices is studied. Assuming that the boundary conditions are reached after a finite number of laminations and using piecewise linear finite…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…