散乱数据带自然边界条件三元多项式样条插值  

TRIVARIATE POLYNOMIAL SPLINE INTERPOLATION WITH NATURAL BOUNDARY CONDITION FOR SCATTERED DATA

作　　者：徐应祥[1,2] 喻高航[3] 关履泰[4] 

机构地区：[1]中山大学新华学院,广州510520 [2]西北师范大学数学与信息科学学院,兰州730070 [3]赣南师范学院数学与计算机科学学院,江西赣州341000 [4]中山大学科学计算与计算机应用系,广州510275

出　　处：《计算数学》2011年第4期423-446,共24页Mathematica Numerica Sinica

基　　金：国家自然科学基金项目(11001060)

摘　　要：为解决4维散乱数据Hermit-Birkhoff型插值问题,在使给定的目标泛极小的条件下,构造了一种带自然边界条件的三元多项式样条函数方法,研究了插值问题解的特征,存在唯一性,收敛性及误差,最后给出了一些数值算例.To solve the interpolation problem of Hermit-Birkhoff type for scattered data of 4D, under the condition of minimizing the given functional, a new trivatiate polynomial spline interpolation with natural conditions have been constructed. The characterization, existence, uniqueness, convergence and error estimation of the solution of the interpolation problem have been studied carefully. Some numerical examples have been presented at last to illustrate the method.

关 键 词：散乱数据 自然边界条件 三元多项式 自然样条 

分 类 号：O174.14[理学—数学]