三奇次散乱点多项式自然样条插值

TRIVARIATE ODD DEGREE POLYNOMIAL NATURAL SPLINE INTERPOLATION FOR SCATTERED DATA

为解决较为复杂的三变量散乱数据插值问题,提出了一种三元多项式自然样条插值方法.在使得对一种带自然边界条件的目标泛函极小的情况下,用Hilbert空间样条函数方法,构造出了插值问题的解,并可表为一个分块三元三奇次多项式.其表示形式简单,且系数可由系数矩阵对称的线性代数方程组确定.

To solve the complicated interpolation problem for trivariate scattered data, a trivariate polynomial natural spline interpolation method is proposed. In the case of minimizing the objective functional with natural boundary conditions, the solution of the interpolation problem is constructed by the spline function methods of Hilbert space and in every block is a trivariate odd degree polynomial. Its expression is so simple and the coefficients can be decided by a linear system whose coefficient matrix is symmetry.