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It is well-known that the univariate Multiquadric quasi-interpolationoperator is constructed based on the piecewise linear interpolation by |x|. Inthis paper, we first introduce a new transcendental RBF based on the hyperbolictangent function as a smooth approximant to f(r)=r with higher accuracy andbetter convergence properties than the multiquadric. Then Wu-Schaback'squasi-interpolation formula is rewritten using the proposed RBF. It preservesconvexity and monotonicity. We prove that the proposed scheme converges with arate of O(h^2). So it has a higher degree of smoothness. Some numericalexperiments are given in order to demonstrate the efficiency and accuracy ofthe method.

A shape preserving quasi-interpolation operator based on a new transcendental RBF