Wepropose a new approximation technique forHybridAutomata. Given anyHybridAutomatonH, we callApprox(H , k) the Polynomial Hybrid Automaton obtained by approximating each formula in H with the formulae k obtained by replacing the functions in with their Taylor polynomial of degree k. We prove that Approx(H , k) is an over-approximation ofH. We study the conditions ensuring that, given any > 0, s...

This paper presents a new approach to the functional approximation of the M/G/1/N built on a Taylor series approach. Specifically, we establish an approximative expression for the remainder term of the Taylor series that can be computed in an efficient manner. As we will illustrate with numerical examples, the resulting Taylor series approximation turns out to be of practical value.

A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.

In [10, 11] we proposed a technique to approximate Hybrid Automata (HA) with Polynomial HA. The idea was to replace functions appearing in formulae with their Taylor Polynomials. Here we extend this technique to HA with formulae admitting integral functions. We prove that we get over-approximations of the original HA. We study the conditions ensuring that: 1. the “distance” between the formulae...

Abstract We describe an expansion of Legendre polynomials, analogous to the Taylor expansion, to approximate arbitrary functions. We show that the polynomial coefficients in Legendre expansion, thus, the whole series, converge to zero much more rapidly compared to the Taylor expansion of the same order. Furthermore, using numerical analysis with sixth-order polynomial expansion, we demonstrate ...

A Taylor series approximation to multivariate integrals taken with respect to a multivariate probability distribution is proposed and applied to the computation of multivariate normal probabilities and conditional expectations. The approximation does not require that the multivariate distribution have a structured covariance matrix and, in its simplest form, can be written as the product of uni...

One of the most common and practical ways of representing a real function on machines is by using a polynomial approximation. It is then important to properly handle the error introduced by such an approximation. The purpose of this work is to offer guaranteed error bounds for a specific kind of rigorous polynomial approximation called Taylor model. We carry out this work in the Coq proof assis...