Résumé : Nous étudions dans cet article des algorithmes de calcul de la réduction de Hermite d'une matrice a coefficients polynomiaux, qui évitent l'explosion de la taille des objets intermédiaires et ont une bonne complexité séquentielle. Le deuxième et le troisième algorithmes généralisent la méthode des sous-résultants pour le calcul du pgcd de deux polynomes. Le dernier de ces algorithmes s...

In this paper we prove some inequalities for convex function of a higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrovi c's inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial je H (x)j in ter...

A method for obtaining the correlation of atwo Hermite neural network is developed. The method is based on the fact that a Hermite function is unchanged by the Fourier transform, which allows an expression for the correlation to be obtained directly from the network weights without the need for the Fourier transform. Comparative results with other neural network correlation methods are presente...

Abstract Integrals involving products of Hermite polynomials with the weight factor exp (−x2) over the interval (−∞,∞) are considered. A result of Azor, Gillis and Victor (SIAM J. Math. Anal. 13 (1982) 879–890] is derived by analytic arguments and extended to higher order products. An asymptotic expansion in the case of a product of four Hermite polynomials Hn(x) as n → ∞ is obtained by a discr...

By using the algorithm of Nfimberger and Riessinger (1995), we construct Hermite interpolation sets for spaces of bivariate splines Sq(d 1 ) of arbitrary smoothness defined on the uniform type triangulations. It is shown that our Hermite interpolation method yields optimal approximation order for q >~ 3.5r + 1. In order to prove this, we use the concept of weak interpolation and arguments of Bi...

The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed. 2000 Mathematics subjec...

3D rotation invariants based on orthogonal Gaussian–Hermite moments are proposed in this paper. We present an elegant and easy theoretical derivation of them. At the same time we prove by experiments that the Gaussian–Hermite invariants have better numerical stability than the traditional invariants composed of geometric moments. © 2014 Elsevier B.V. All rights reserved. d a w s i i d r [ t m i...

Using the basis of Hermite–Fourier functions (i.e. the quantum oscillator eigenstates) and the Sturm theorem, we derive constraints for a function and its Fourier transform to be both real and positive. We propose a constructive method based on the algebra of Hermite polynomials. Applications are extended to the 2-dimensional case (i.e. Fourier–Bessel transforms and the algebra of Laguerre poly...

We present a tension-controlled 2-point Hermite interpolatory subdivision scheme that is capable of reproducing circles starting from a sequence of sample points with any arbitrary spacing and appropriately chosen first and second derivatives. Whenever the tension parameter is set equal to 1, the limit curve coincides with the rational quintic Hermite interpolant to the given data and has guara...