Тип публикации: статья из журнала
Год издания: 2004
Идентификатор DOI: 10.1016/j.cam.2003.12.024
Ключевые слова: cubature; multivariate integrals; spherical designs, Cubature, Multivariate integrals, Spherical designs, Constant weight function, Cubature formulae, Functions, Computational methods, mathematical method
Аннотация: In this note cubature formulae of degree 5 are studied for n-dimensional integrals over the ball with constant weight function. We apply the method of reproducing kernel to show that the existence of such formulae attaining the best known lower bound is equivalent to the existence of tight spherical 5-designs. The known results conПоказать полностьюcerning spherical 5-designs show that the lower bound for the integral under consideration will not be attained in general. The bound will be attained for n = 213, 7,23 and possibly for n = (2p + 1)(2) -2, p > 5. In all other cases the bound must be increased at least by 1, in particular, Stroud's formulae for n = 4,5,6,7 are minimal. (C) 2004 Elsevier B.V. All rights reserved.
Журнал: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Выпуск журнала: Vol. 169, Is. 2
Номера страниц: 247-254
ISSN журнала: 03770427
Место издания: AMSTERDAM
Издатель: ELSEVIER SCIENCE BV