一种C^1连续的二元有理三次插值样条（英文）  

A C^1 bivariate rational cubic interpolating spline

作　　者：王冬银[1] 陶有田[1,2,3] 

机构地区：[1]巢湖学院应用数学学院,安徽巢湖238000 [2]中国科学技术大学数学科学学院,安徽合肥230026 [3]安徽富煌钢构,安徽合肥238076

出　　处：《中国科学技术大学学报》2017年第3期204-213,共10页JUSTC

基　　金：Supported by the Nation Natural Science Foundation of China(11472063);the Provincial Natural Science Research Program of Higher Education Institutions of Anhui Province(KJ2013A194,KJ2013Z230);Anhui Province Colleges and Universities Outstanding Youth Talent Support Program(gxyq ZD2016285)

摘　　要：利用矩形域上的函数值及偏导数值作为插值数据,构造了一种带6个形状参数、分母为双二次的二元有理三次插值样条,讨论了其C^1连续条件,给出了诸如对称性的一些性质,证明了其有界性并作了误差分析.最后给出了一个数值例子说明了形状参数对于曲面构造的有效性.A bivariate rational bicubic interpolating spline（BRIS） with hiquadratic denominator and six shape parameters was constructed using both function values and partial derivatives of the function as the interpolation data in a rectangular domain. The C^1 continuous condition of BRIS was discussed. Some properties of BRIS such as symmetry were given. BRIS was proved to be bounded and its error was estimated. In the end, a numerical example was given to illustrate the effect of the shape parameters on the shape of BRIS surface.

关 键 词：二元有理三次插值样条 形状参数 有界性 误差估计 对称性 

分 类 号：O241.5[理学—计算数学] O231.1[理学—数学]