Hermite Orthogonal Polynomials of a Discrete Variable

Article type: Research Article

Authors: Streltsova, O.I.^{a; 1; 2} | Streltsov, I.P.^b

Affiliations: [a] Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia | [b] Higher Mathematics, Vladivostok State University of Economy, Service (VSUES), 41 Gogolya St., Vladivostok, 690600 Russia

Correspondence: [2] The address for manuscript correspondence: O.Streltsova, LIT, JINR, Dubna, Moscow region, 141980, Russia. Fax: (09621) 65145. Tel: (09621) 64425. E-mail: strel@thsun1.jinr.ru.

Note: [1] E-mail: strel@thsun1.jinr.ru.

Abstract: The Hermite orthogonal polynomials on a discrete point set are constructed. A discrete point set, a weight function and normalizing factors are obtained, and the orthogonality of them is proved. The problems of an approximation of functions by one, two and three variables with the help of interpolation of the Hermite series constructed on the appropriate discrete point set are considered.

Keywords: Orthogonal polynomials on a discrete point set, Hermite polynomials, approximation

DOI: 10.3233/JCM-2002-21-233

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 2, no. 1-2, pp. 237-244, 2002