In this paper, a kind of Bernoulli-type operator is proposed by combining a univariate multiquadric quasi-interpolation operator with the generalized Taylor polynomial. With an assumption on the shape-preserving parameter c, the convergence rate of the new operator is derived, which indicates that it could produce the desired precision. Numerical comparisons show that this method offers a higher degree of accuracy. Moreover, the associated algorithm is easily implemented.
radial basis functions; multiquadrics; quasi-interpolation; Bernoulli polynomials; convergence rate
