积分值五次样条拟插值

On Integro Quintic Spline Quasi-interpolation

为了解决连续区间上积分值的函数重构,提出一种直接构造方法.首先利用积分值的线性组合得到结点处函数值的六阶逼近;然后将该近似函数值代入到传统的五次离散样条拟插值算子的泛函值上,得到积分值五次样条插值;最后基于五次样条拟插值的收敛阶,得到该方法对高阶导数逼近的收敛阶.实验结果表明,与传统的积分值样条插值方法相比,该方法简单、有效,可以推广到积分值高次样条拟插值上.

In order to reconstruct function from the integral values of successive subintervals,a kind of direct construction method is proposed.Firstly,the function values at the knots with six order approximation from the linear combination of the integral values are derived.Secondly,the approximated function values are plugged into the values of linear functional in quintic discrete spline quasi-interpolation operators and so-called integro quintic spline quasi-interpolation is constructed.Finally,the error estimate for approximating higher order derivative is obtained with the benefit of the convergence order of traditional spline quasi-interpolation.Experiments show that our proposed method performs simpler and more effective than traditional integro spline interpolation.Moreover,it can be easily generalized to integro spline quasi-interpolation of higher degree.