Sets of lattice cubature rules that are optimal in terms of the number of nodes and exact on trigonometric polynomials in three variables | Научно-инновационный портал СФУ

## Sets of lattice cubature rules that are optimal in terms of the number of nodes and exact on trigonometric polynomials in three variables

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 asymptotically 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".

#### Издание

Журнал: Computational Mathematics and Mathematical Physics

Выпуск журнала: Vol. 45, Is. 2

Номера страниц: 202-212

#### Авторы

• Osipov N.N. (Krasnoyarsk State Technical University, ul. Kirenskogo 26, Krasnoyarsk, 660074, Russian Federation)

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