The region of absolute stability of multistep multiderivative methods is studied in a neighborhood of the origin. This leads to a necessary condition for Astability. For methods where p(f)/(f 1) has no roots of modulus 1 this condition can be checked very easily. For Hermite interpolatory and Adams type methods a necessary condition for A -stability is found which depends only on the error orde...

In this paper, we derive a result concerning eigenvector for the product of two operators defined on a Lie algebra of endomorphisms of a vector space. The results given by Radulescu, Mandal and authors follow as special cases of this result. Further using these results, we deduce certain properties of generalized Hermite polynomials and Hermite Tricomi functions. 2000 Mathematics Subject Classi...

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...

The Bernstein-Bézier representation of polynomials is a very useful tool in computer aided geometric design. In this paper we make use of (multilinear) tensors to describe and manipulate multivariate polynomials in their Bernstein-Bézier form. As application we consider Hermite interpolation with polynomials and splines.

The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for large values of indices are found. The applications to the squeezed one-mode states and to the time-dependent quantum harmonic oscillator are considered.

By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Tra...

For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a symmetric scheme and a non-symmetric scheme. The general approach is illustrated by the examples of the classical orthogonal polynomials: Hermite, Jacobi and La...

The aim of this paper is to define and study of the Gegenbauer matrix polynomials of two variables. An explicit representation, a three-term matrix recurrence relations, differential recurrence relations and hypergeometric matrix representation for the Gegenbauer matrix polynomials of two variables are given. The Gegenbauer matrix polynomials are solutions of the matrix differential equations a...

Ben-yu Guo a,∗, Jie Shen b,c,∗∗ and Cheng-long Xu d a School of Mathematical Sciences, Shanghai Normal University, Shanghai, 200234, P.R. China E-mail: [email protected] b Department of Mathematics, Xiamen University, Xiamen, 361005, P.R. China c Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA E-mail: [email protected] d Department of Applied Mathematics, Tongji ...

We present a convergent asymptotic formula for the zeros of the Hermite functions as λ → ∞. It is based on an integral formula due to the authors for the derivative of such a zero with respect to λ. We compare our result with those for zeros of Hermite polynomials given by P. E. Ricci.