Сибирский федеральный университет

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 concerning 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

• Noskov M.V. (KRASNOYARSK STATE UNIV)
• Schmid H.J. (KRASNOYARSK STATE UNIV)

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