Related papers: On Wu and Schaback's Error Bound

In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…

We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…

This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation. We provide bounds for the generalization and training error in terms of the width of the network's layers and the…

We revisit a recent discussion about the boundary condition at the origin in the Schroedinger radial equation for central potentials. Using a slight modification of the usual spherical coordinates, the origin of a previously reported Dirac…

It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…

Contrary to an assumption made by Bojanczyk, Higham, and Patel [SIAM J. Matrix Anal. Appl., 24(4):914-931, 2003], a perturbation bound for indefinite least square problems is capable of arbitrarily large overestimates for all perturbations…

We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion. We prove lower error…

The single exponential (SE) and double exponential (DE) formulas are widely recognized as efficient quadrature formulas for evaluating integrals with endpoint singularity. For integrals exhibiting algebraic singularity, explicit error…

In this note we consider inequalities involving the error function $\phi$. Our methodes give new proofs of some known inequalities of Komatsu, and of Szarek and Werner, and also produce two families of inequalities that give upper and lower…

In this paper, we obtain sharp bounds for the norm of pre--Schwarzian derivatives of certain analytic functions. Initially this problem was handled by H. Rahmatan, Sh. Najafzadeh and A. Ebadian [Stud Univ Babe\c{s}--Bolyai Math {\bf61}(2):…

We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes…

Lavrik and the author gave uniform bounds of the error term in the approximate functional equation for the derivatives of the Hardy's Z-function. We obtain a new bound of this error term which is much better for high order derivatives.

The paper deals with the basic integral equation of random field estimation theory by the criterion of minimum of variance of the error estimate. This integral equation is of the first kind. The corresponding integra$ operator over a…

We discuss conformal manifolds for conformal field theories with boundaries or defects. Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions…

A recent line of works, initiated by Russo and Xu, has shown that the generalization error of a learning algorithm can be upper bounded by information measures. In most of the relevant works, the convergence rate of the expected…

In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…

This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…

Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…

We present a comprehensive study of radial basis function (RBF) approximations for elliptic and obstacle-type boundary value problems under a variational formulation. Our focus is on practical accuracy, robustness and efficiency. To address…

The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet…