| 書目名稱 | The Theory of Cubature Formulas | | 編輯 | S. L. Sobolev,V. L. Vaskevich | | 視頻video | http://file.papertrans.cn/922/921110/921110.mp4 | | 叢書名稱 | Mathematics and Its Applications | | 圖書封面 |  | | 描述 | This volume considers various methods for constructing cubatureand quadrature formulas of arbitrary degree. These formulas areintended to approximate the calculation of multiple and conventionalintegrals over a bounded domain of integration. The latter is assumedto have a piecewise-smooth boundary and to be arbitrary in otheraspects. Particular emphasis is placed on invariant cubature formulasand those for a cube, a simplex, and other polyhedra. Here, thetechniques of functional analysis and partial differential equationsare applied to the classical problem of numerical integration, toestablish many important and deep analytical properties of cubatureformulas. The prerequisites of the theory of many-dimensional discretefunction spaces and the theory of finite differences are conciselypresented. Special attention is paid to constructing and studying theoptimal cubature formulas in Sobolev spaces. As an asymptoticallyoptimal sequence of cubature formulas, a many-dimensional abstractionof the Gregory quadrature is indicated. ..Audience:. This book is intended for researchers having a basicknowledge of functional analysis who are interested in theapplications of modern theoretical meth | | 出版日期 | Book 1997 | | 關(guān)鍵詞 | Numerical integration; cubature; functional analysis; numerical analysis | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-015-8913-0 | | isbn_softcover | 978-90-481-4875-2 | | isbn_ebook | 978-94-015-8913-0 | | copyright | Springer Science+Business Media Dordrecht 1997 |
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