A novel parameterized multiquadric quasi-interpolation operator with its optimal parameters

The shape parameter c plays a crucial role in determining the accuracy and effectiveness of multiquadric quasi-interpolation algorithm. However, a few works discuss the shape parameter c in multiquadric quasi-interpolation operator. In this paper, a novel univariate parameterized multiquadric quasi-interpolation operator is proposed, which is a generalization of Chen’s quasi-interpolation scheme. The parameterized multiquadric quasi-interpolation exhibits high accuracy and excellent shape-preserving properties. Furthermore, we present the error analysis of the parameterized multiquadric quasi-interpolation operator, which achieves the same convergence order as Wu’s quasi-interpolation scheme. Furthermore, an algorithm for selecting the optimal parameters in the multiquadric quasi-interpolation operator is developed. Finally, several numerical examples are given to verify the expected approximation capabilities of the proposed parameterized quasi-interpolation operator by comparing it with Chen’s quasi-interpolation scheme. Additionally, the developed algorithm for parameter selection has proven effective.