Abstract: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 an smooth approximant to φ(r) = r with higher accuracy and better convergence properties than the MQ RBF √ r 2 + c 2 . Then the Wu-Schaback's quasi-interpolation formula is rewritten using the proposed RBF. It preserves convexity and monotonicity. We prove that the … Show more
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