Related papers: Peano-like bounds for some Newton-Cotes formulae
The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
Split-Plot or Repeated Measures Designs with multiple groups occur naturally in sciences. Their analysis is usually based on the classical Repeated Measures ANOVA. Roughly speaking, the latter can be shown to be asymptotically valid for…
Absolute value equations, due to their relation to the linear complementarity problem, have been intensively studied recently. In this paper, we present error bounds for absolute value equations. Along with the error bounds, we introduce an…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many…
We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to different norms of the function are proven. By the estimation the well known…
The quality of the narrow-width approximation is examined for partonic and convolved cross sections of sample processes. By comparison with accurate predictions significant limitations are revealed.
We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity…
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…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
We show that the Flatte formula is not adequate to interpret precision data on a resonance production near an inelastic threshold. A unitary parameterization, satisfying generalized Watson's theorem for the production amplitudes, is…
We construct several sequences of asymptotically optimal definite quadrature formulae of fourth order and evaluate their error constants. Besides the asymptotical optimality, an advantage of our quadrature formulae is the explicit form of…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
Error estimation is given for a regularized Shannon's sampling formulae, which was found to be accurate and robust for numerically solving partial differential equations.
We provide quantitative gradient bounds for solutions to certain parabolic equations with unbalanced polynomial growth and non-smooth coefficients.
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
We provide a general constrained risk inequality that applies to arbitrary non-decreasing losses, extending a result of Brown and Low [Ann. Stat. 1996]. Given two distributions $P_0$ and $P_1$, we find a lower bound for the risk of…
We study multiplicative inequalities among entries of Lorentzian matrices, referred to as bounded ratios. These inequalities can be viewed as generalizations of the classical Alexandrov--Fenchel inequalities for mixed volumes. Our main…
In contrast to a maximum-likelihood decoder, it is often desirable to use an incomplete decoder that can detect its decoding errors with high probability. One common choice is the bounded distance decoder. Bounds are derived for the total…