CAJ | 학술논문

考虑对窄间散乱数据(2m-1,2n-1)次多项式自然样条插值,使得插值函数对x的m次偏导数和对y的n次偏导数平方积分极小(带自然边界条件).用希尔伯特空间样条方法,得出其解的结构,解的系数能够用线性方程组确定,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.
고필대착간산란수거(2m-1,2n-1)차다항식자연양조삽치,사득삽치함수대x적m차편도수화대y적n차편도수평방적분겁소(대자연변계조건).용희이백특공간양조방법,득출기해적결구,해적계수능구용선성방정조학정,방정조계수구진대칭,가용개진적평방근법해.례자표명방법간단,효과량호.
(2m- 1, 2n - 1) degree polynomial natural splines interpolations for space scattered data such that the integral of square of partial derivative of m orders to x and n orders to y for the interpolating function is minimal(with natural boundary conditions). The solution is constructed as the sum of a (m - 1, n - 1) degree polynomial and piecewise (2m - 1, 2n - 1) degree polynomial by Hilbert space spline function methods. Its coefficients can be decided by a linear system. The coefficient matrix is so symmetry that the improved square root method can be successed. Results are very simple and can be achieved easily in computer programs.