摘要
函数插值的理论与方法在科研生产实践中的应用(多元函数列表、工业产品外形设计、地球资源探索及曲面设计的有限元法等)一直是计算数学专业研究领域的一个研究热点.针对在工业生产和日常生活中常用的二次曲面椭圆抛物面来研究其上的多元切触(Hermite)插值问题,给出了定义于椭圆抛物面上的切触插值的正则性问题提法.然后对插值条件组的拓扑结构进行了较为深入的研究,得到了定义于椭圆抛物面上的切触插值正则条件组的判定定理及构造方法,并给出了定理证明.最后以实验算例验证了算法的有效性.
Abstract
The combination of interpolation problem and production practice has been a research hots-pot in the research field of computational mathematics majors.The results have been widely used in various fields(list of multivariate functions,design of industrial product shapes,exploration of earth's resources and disaster laws,and finite element method for surface design.).In this paper,we study the multivariate contact interpolation(Hermite interpolation)problem on a quadratic elliptic parabo-loid,which is commonly used in industrial production and daily life.We give a formulation of the regularity problem of Hermite interpolation on an elliptic paraboloid,by a deeper in-depth study on the topology of the interpolating condition group.We obtain a decision theorem and a construction method for the group of the multivariate contact interpolation regular conditions defined on an elliptic paraboloid,give a proof of the theorem,and finally verify the effectiveness of the algorithm with an experimental example.
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