一种散乱点双三次多项式自然样条插值

 考虑对空间散乱点的一种双三次多项式样条插值, 使得插值函数对x与对y的二阶偏导数平方积分极小(带自然边界条件)。用希氏空间样条方法，得出其解可表为一个双一次多项式与分片双三次多项式之和。它的系数能够用线性代数方程组确定,方程组系数矩阵对称,可用改进的平方根法解。例子表明方法简单,效果良好。

Interpolation for Space Scattered Data by Bicubic Polynomial Natural Splines

Bicubic splines interpolate for space scattered data such that the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). The solution is constructed as the sum of a bilinear polynomial and piecewise bicubic polynomials by Hilbert space spline function methods. Its coefficients can be decided by a linear system.The coefficient matrix is so symmetry that the LDLT method can be successed.Results are very simple and can be achieved easily in computer programs.