散乱数据带自然边界条件三元多项式光顺样条

摘要

考虑对4维空间散乱数据的一种带自然边界条件的样条光顺.为使得给定的目标泛函达到极小,用Hilbert空间样条函数方法,得出其解可表为一个分片三元多项式,其表示形式简单,且系数可由线性代数方程组确定.最后给出一些数值例子进行了验证.%A spline smoothing method with natural boundary conditions for scattered data of 4D are considered. In order to minimization the given objective functional, using the spline function methods of Hilbert space, the solution is constructed as a piecewise tri-variable polynomial. Its expression is so simple and the coefficients are decided by a linear system. Some numerical examples are presented to illustrate the method.