Тип публикации: статья из журнала
Год издания: 2005
Ключевые слова: Lattice cubature rules, Optimal cubature rules, Trigonometric polynomials in three variables
Аннотация: Sets of lattice cubature rules with the lattice of nodes ?k = Mk?, where the lattice M k is generated by the matrix kB + C (B and C are integer square matrices of order n independent of k and det(B) ? 0) are considered. At n = 3, for each integer r (-4 ? r ? 1), the set S(min) with the trigonometric (6k + r) property and the asymptПоказать полностьюotically minimal number of nodes N(min)(k) is found. This means that, for any set S(min) with the trigonometric (6k + r) property and the number of nodes N(k), the inequality N(k) ? N(min)(k) holds true if k is sufficiently large. Certain properties of the optimal sets S(min) and the nearest (in terms of the number of nodes) sets S(min+) are investigated. Copyright © 2005 by MAIK "Nauka/Interperiodica".
Журнал: Computational Mathematics and Mathematical Physics
Выпуск журнала: Vol. 45, Is. 2
Номера страниц: 202-212