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 $c$ , which indicates that our operators could provide the desired smoothness and precision by choosing a suitable value of $c$ . 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.