中文摘要：

应用随机分布的节点集进行函数逼近时,点的支撑域的大小对逼近的有效性及精度有很大影响.为研究移动最小二乘法中最优的支撑域半径,首先给出了一种全新的节点密度的概念,它不仅能刻画节点分布的疏密程度,而且其计算算法简单,也便于点的支撑域半径的选取;其次,基于节点密度的概念给出了搜索支撑域内节点的领域搜索算法,与通常使用的全域搜索算法相比,领域搜索算法提高了计算效率,节省了搜索节点需要的时间;最后给出算例,验证文中提出的计算点的支撑域半径算法的有效性.

英文摘要：

When a randomly distributed set of nodes is used for function approximation,the radius of support domain of a point has a great influence on the validity and accuracy of approximation.In order to help to find the optimal radius of the support domain for moving least square method,a new notion of the node density is proposed in this paper firstly.For any given point,it is simple to calculate its density,and easy to find a proper radius of support domain.Secondly,based on the notion of density,a new neighborhood search algorithm suitable for both uniform and random distributed node sets,named as leading search,is proposed for search a given number of nodes near a point.Compared to the commonly used global search algorithm,the leading search algorithm improves the efficiency of computation and saves the time required for the node search.Finally,numerical examples are presented to verify the validity of the algorithm.