It is well-known that the univariate Multiquadric quasi-interpolation operator is constructed based on the piecewise linear interpolation by |x|. In this paper, we first introduce a new transcendental RBF based on the hyperbolic tangent function as a smooth approximant to f(r)=r with higher accuracy and better convergence properties than the multiquadric. Then Wu-Schaback's quasi-interpolation formula is rewritten using the proposed RBF. It preserves convexity and monotonicity. We prove that the proposed scheme converges with a rate of O(h^2). So it has a higher degree of smoothness. Some numerical experiments are given in order to demonstrate the efficiency and accuracy of the method.

翻译：众所周知,单等离子多赤道准内插操作器是根据 ⁇ x ⁇ 的片度线性内插构建的。在本文中,我们首先引入一个新的超光性RBF, 其基础是双曲正切函数, 光滑近似正切函数, 精度和趋同特性高于多方的f(r)=r。 然后, Wu-Schaback的准内插公式使用拟议的RBF改写。 它保存了共性和单调性。 我们证明, 拟议的方案与O(h)2的速率趋同, 因此它具有更高程度的顺畅度。 为了展示方法的效率和准确性, 进行了一些数字实验。