一种新的积分值型MQ拟插值算子

A New Integral-Valued MQ Quasi-Interpolation Operator

摘要: Multiquadric (MQ)函数作为径向基函数的一种，其作为核函数可逼近任何光滑函数，被广泛应用在拟插值的研究中，现有的MQ拟插值大部分都是以离散函数值为已知条件，而在实际应用中，积分值作为已知条件也比较常见，为了让MQ拟插值得到更广泛的应用，本文提出了一种新的基于积分值的MQ拟插值算子。首先利用连续区间上积分值的线性组合来对节点处的导数值进行逼近，然后根据已有的MQ拟插值进一步得到新的积分值型MQ拟插值算子，并给出了误差估计。最后通过数值实验展示了本文构造的积分值型MQ拟插值算子的逼近效果，说明了该方法的可行性和有效性。

Abstract: As a kind of radial basis function, Multiquadric (MQ) function, as a kernel function, can approximate any smooth function, and is widely used in the research of quasi-interpolation. Most of the existing MQ quasi-interpolation is based on the known condition of the discrete function value, and in practical applications, the integral value is also a common-known condition. In order to make MQ quasi-interpolation more widely used, a new MQ quasi-interpolation operator based on integral value is proposed in this paper. First, the derivative value at the node is approximated by the linear combination of integral values on the continuous interval, and then a new integral value MQ quasi-interpolation operator is obtained according to the existing MQ quasi-interpolation, and the error estimate is given. Finally, the approximation effect of the integral-valued MQ quasi-interpolation operator constructed in this paper is demonstrated by numerical experiments, and the feasibility and effectiveness of the proposed method are demonstrated.