有理三次Hermite插值样条及其逼近性质  

Rational Cubic Hermite Interpolating Spline and its Approximation Properties

作　　者：谢进[1,2] 檀结庆[2] 李声锋[3] 

机构地区：[1]合肥工业大学计算机与信息学院,合肥230009 [2]合肥学院数学与物理系,合肥230601 [3]蚌埠学院数学与物理系,蚌埠233000

出　　处：《工程数学学报》2011年第3期385-392,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61070227);教育部科学技术研究重大项目(309017);教育部博士点基金(20070359014);安徽省教育厅教研重点项目(20100935);合肥学院科研重点项目(11KY02ZD)~~

摘　　要：提高插值曲线曲面的逼近性是计算辅助几何设计中的一个重要问题.本文构建了一种带单参数的分段有理三次Hermite插值样条.讨论了该样条的逼近性,给出了一种提高插值曲线曲面逼近性的方法,并且给出数值例子.结果表明,对于给定的插值条件,通过选择合适的参数,依本文方法所生成的插值曲线曲面在逼近效果上好于标准三次Hermite插值曲线曲面.Improving the approximability of interpolating curves/surfaces is an important issue in the computer aided geometric design.A piecewise rational cubic Hermite interpolating spline with a single parameter is constructed in this paper.The approximation properties of the interpolating spline are studied and a method for improving the approximability of the curves/surfaces is introduced.Examples are given to illustrate the advantages of our method.The results show that,for given interpolating conditions,if the parameters are chosen properly,the introduced interpolating curves/surfaces can approximate the interpolated functions better than the standard cubic Hermite interpolating curves/surfaces.

关 键 词：有理三次Hermite样条 三次Hermite样条 Peano-Kernel定理 形状参数 逼近性 

分 类 号：O174.41[理学—数学]