一类二维样条函数的最佳误差估计  

Optimal Error Estimation of a Class of Two-Dimensional Spline Interpolation Function

作　　者：唐月红[1] 许有信[1] 

机构地区：[1]南京航空航天大学数理力学系

出　　处：《南京航空航天大学学报》1993年第4期568-574,共7页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：本文对一类非均匀二维插值样条的研究,得出了矩形域R上双三次插值样条函数x(u,w),当满足条件时,在矩形域R边界上节点处的三阶和四阶混合偏导数的估计式,推广了均匀分划情形的结果,获得了精确的误差估计。The main result of the present paper is the following theorem.Let x(u,w)be the two-dimensional Bi-cubic spline interpolating function which is a uniform division in a rectangle,and satisfies (5) of the Reference [7],then we have the following estimation equation for the fourth order mixed partial derivatives at the nodes on boundaries of the rectangle.The above inequalities will become equalitres whenare true repectively and.

关 键 词：应用数学 样条插值 插值法 误差 

分 类 号：O241.5[理学—计算数学]