High accuracy multiquadric quasi-interpolation

In this paper, we propose a new multilevel univariate multiquadric (MQ) quasi-interpolation approach with higher approximation order compared with the existing MQ quasi-interpolations. The proposed approach includes two schemes, which are based on inverse multiquadric radial basis function (IMQ-RBF) interpolation, and Wu & Schaback’s MQ quasi-interpolation operator LDLD. Error analysis shows that our operators produce higher accuracy. Numerical examples demonstrate that the proposed MQ quasi-interpolation schemes are valid.