Construction of cubature formulae with preassigned nodes§
Zhongxuan Luo, Zhaoliang Meng, Fengshan Liu · Applicable Analysis · 2008
In this article, a technique for developing cubature rules with preassigned nodes is presented to avoid wasting of information in scientific computation. The corresponding constructive method of the cubature rule is also given. As an application of the rules, a cubature formula on disk, which was derived via the method of reproducing kernel in (Xu, Y., 2000, Constructing cubature formulae by the method of reproducing kernel. Numerische Mathematik, 85, 155–173), is reconstructed by using our technique. When the preassigned nodes are selected as the nodes of a cubature formula of lower degree, an embedded cubature formula can be easily obtained by the presented method. Furthermore, some examples are included in the article.