| Автор | Cools, Ronald |
| Дата выпуска | 1997 |
| dc.description | In this paper we present a general, theoretical foundation for the construction of cubature formulae to approximate multivariate integrals. The focus is on cubature formulae that are exact for certain vector spaces of polynomials. Our main quality criteria are the algebraic and trigonometric degrees. The constructions using ideal theory and invariant theory are outlined. The known lower bounds for the number of points are surveyed and characterizations of minimal cubature formulae are given. We include references to all known minimal cubature formulae. Finally, some methods to construct cubature formulae illustrate the previously introduced concepts and theorems. |
| Формат | application.pdf |
| Издатель | Cambridge University Press |
| Копирайт | Copyright © Cambridge University Press 1997 |
| Название | Constructing cubature formulae: the science behind the art |
| Тип | research-article |
| DOI | 10.1017/S0962492900002701 |
| Electronic ISSN | 1474-0508 |
| Print ISSN | 0962-4929 |
| Журнал | Acta Numerica |
| Том | 6 |
| Первая страница | 1 |
| Последняя страница | 54 |
| Аффилиация | Cools Ronald; Katholieke Universiteit Leuven |
