A kind of improved univariate multiquadric quasi-interpolation operators

In this paper, a kind of improved univariate multiquadric quasi-interpolation operators is proposed by using Hermite interpolating polynomials. Error analysis shows that the convergence rate of the operators depends heavily on the shape parameter cc, which indicates that our operators could provide the desired smoothness and precision by choosing a suitable value of cc. Numerical examples show that the operators provide a high degree of accuracy. Moreover, operators are applied to the fitting of discrete solutions of initial value problems.