Related papers: An Improved Error Bound for Multiquadric and Inver…
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…
We present a brief survey of existing mistake bounds and introduce novel bounds for the Perceptron or the kernel Perceptron algorithm. Our novel bounds generalize beyond standard margin-loss type bounds, allow for any convex and Lipschitz…
In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval…
We propose and prove an existential theorem for entanglement-assisted asymmetric quantum error correction. Then we demonstrate its superiority over the conventional one.
We give an improved lower bound for the $L_2$-discrepancy of finite point sets in the unit square.
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
Exponential error bounds achievable by universal coding and decoding are derived for frame-asynchronous discrete memoryless %asynchronous multiple access channels with two senders, via the method of subtypes, a refinement of the method of…
We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the…
An explicit upper bound is derived for the modulus of divided difference for a smooth(not necessarily analytic) function defined on a smooth Jordan arc (or a smooth Jordan curve) in the complex plane. As an immediate application, an error…
How good is a triangulation as an approximation of a smooth curved surface or manifold? We provide bounds on the {\em interpolation error}, the error in the position of the surface, and the {\em normal error}, the error in the normal…
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…
The main contribution of this paper is a new improved variant of the laser method for designing matrix multiplication algorithms. Building upon the recent techniques of [Duan, Wu, Zhou, FOCS 2023], the new method introduces several new…
Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and…
The threshold estimate derived in previous versions of this paper was incorrect; this note explains the flaw. A new proof is discussed in arXiv:0809.5063.
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…
In this paper, the a posteriori error estimates of the exponential midpoint method for time discretization are studied for linear and semilinear parabolic equations. Using the exponential midpoint approximation defined by a continuous and…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at…
In this paper, we focus on a special class of ideal projectors. With the aid of algebraic geometry, we prove that for this special class of ideal projectors, there exist "good" error formulas as defined by C. de Boor. Furthermore, we…
We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the diameter of a simplex and a geometric parameter. In the…