Related papers: An Improved Error Bound for Multiquadric and Inver…
Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the…
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
It has long been known how to construct radiation boundary conditions for the time dependent wave equation. Although arguments suggesting that they are accurate have been given, it is only recently that rigorous error bounds have been…
This paper derives a new variational equation for the linear least-squares backward error by expressing the backward error in terms of a generalized eigenvalue problem and using results from indefinite linear algebra. For problems with…
We present a new exponential inequality as a generalization of that of Sung \textit{et al.} \cite{sun2011} for $M$-acceptable random variables, and hence for extended negative ones. Our result is based on the simple real inequality $e^{x}…
A straightforward 3-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid…
The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of…
We present an asymptotic limit between correctable and uncor-rectable errors on the Reed-Muller codes of any order. This limit is theoretical and does not depend of any decoding algorithm.
A bound on the error introduced by truncating a quantum addition is given. This bound shows that only a few controlled rotation gates will be necessary to get a reliable computation.
The aim of this paper is to show that, for any $p \in [1,\infty)$, the $W^{1,p}$-anisotropic interpolation error estimate holds on quadrilateral isoparametric elements verifying the maximum angle condition ($MAC$) and the property of…
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…
Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically…
An error analysis for some Newton-Cotes quadrature formulae is presented. Peano-like error bounds are obtained. They are generally, but not always, better than the usual Peano bounds.
A general theory of quantum error avoiding codes is established, and new light is shed on the relation between quantum error avoiding and correcting codes. Quantum error avoiding codes are found to be a special type of highly degenerate…
The performance of maximum-likelihood (ML) decoded binary linear block codes over the AWGN channel is addressed via the tangential-sphere bound (TSB) and two of its recent improved versions. The paper is focused on the derivation of the…
In this paper we present a new family of rules for numerical integration. This family has up to half the error of the widely used Newton-Cotes rules when a sufficient number of points is evaluated and also much better numerical stability…
In this paper the (exponential) perception blunder idea on account of limit locale has been discussed and broke down. For disseminated parameter frameworks of explanatory sort, we demonstrate that, the blunder of state reproduction can be…
This paper extends the earlier work on an oscillating error correction technique. Specifically, it extends the design to include further corrections, by adding new layers to the classifier through a branching method. This technique is still…
We improve on the spectral large sieve inequality for symmetric-squares. We also prove a lower bound showing that the most optimistic upper bound is not true for this family.
This paper introduces a new framework for constructing the Discrete Empirical Interpolation Method DEIM projection operator. The interpolation node selection procedure is formulated using the QR factorization with column pivoting, and it…