连续区间上积分值的MQ拟插值算子

Multiquadric Quasi-Interpolation Operator Based on Integral Values of Successive Subintervals

在某些插值问题中,插值点处的函数值是未知的,而连续区间上的积分值是已知的.如何利用连续区间上积分值信息来解决函数重构是一个重要的问题.首先,文章利用连续区间上积分值的线性组合得到结点处函数值和一阶导数值的的四阶逼近.然后,构造了一类基于连续区间上积分值的MQ拟插值算子,它称之为积分值型MQ拟插值算子.最后,给出了该MQ拟插值算子的整体误差,它具有相应的四阶逼近阶.数值实验表明,该方法是有效可行的.

In some interpolation problems,the function values at the interpolated points are not known,whereas the integral values of some successive intervals are given.How to use the integral values of successive intervals to tackle function reconstruction is an important problem.Firstly,the function values and first-order derivatives at the knots with fourth-order approximation are derived by using the linear combination of the integral values.Secondly,a kind of multiquadric quasiinterpolation operator based on integral values of successive intervals is constructed.It is called integro multiquadric quasi-interpolation operator.Finally,its global error is given and it also possesses fourth-order approximation.Numerical experiments illustrate that the proposed method is flexible and effective.