论文标题
构建阳性插值立方体公式
Constructing Positive Interpolatory Cubature Formulas
论文作者
论文摘要
阳性插值立方体公式（CFS）是为相当一般的整合域和权重功能构建的。这些CF对于包含常数的连续实值函数的通用向量空间是精确的。同时，所有数据点的数量（所有这些数据点都位于集成域内）和立方体权重 - 全部 - 正面 - 较小或等于该向量空间的维度。 Tchakaloff在1957年确保了这种CFS的存在。然而，据作者所知，这项工作是第一个提供成功构建它们的程序的工作。
Positive interpolatory cubature formulas (CFs) are constructed for quite general integration domains and weight functions. These CFs are exact for general vector spaces of continuous real-valued functions that contain constants. At the same time, the number of data points -- all of which lie inside the domain of integration -- and cubature weights -- all positive -- is less or equal to the dimension of that vector space. The existence of such CFs has been ensured by Tchakaloff in 1957. Yet, to the best of the author's knowledge, this work is the first to provide a procedure to successfully construct them.
