A kind of Abel–Goncharov type operators is surveyed. The presented method is studied by combining the known multiquadric quasi-interpolant with univariate Abel–Goncharov interpolation polynomials. The construction of new quasi-interpolants has the property of degree polynomial reproducing and converges up to a rate of . In this study, some error bounds and convergence rates of the combined operators are studied. Error estimates indicate that our operators could provide the desired precision by choosing the suitable shape-preserving parameter c and a nonnegative integer m. Several numerical comparisons are carried out to verify a higher degree of accuracy based on the obtained scheme. Furthermore, the advantage of our method is that the associated algorithm is very simple and easy to implement.

中文翻译：

---

具有较高近似阶次的 Abel-Goncharov 型多二次拟插值算子

考察了一种 Abel-Goncharov 型算子。通过将已知的多二次准插值与单变量 Abel-Goncharov 插值多项式相结合来研究所提出的方法。新的准插值的构造具有 次多项式再现并收敛到一个速率 . 在这项研究中，研究了组合算子的一些误差界限和收敛速度。误差估计表明我们的算子可以通过选择合适的形状保持参数c和非负整数m来提供所需的精度。基于所获得的方案进行了多次数值比较以验证更高程度的准确性。此外，我们方法的优点是相关算法非常简单且易于实现。