A univariate quasi-multiquadric interpolation with better smoothness (Q1770663)

A univariate quasi-interpolation scheme is proposed which is derivative-free and efficient. Since it is a quasi-interpolation method, no linear systems need to be solved for computing the required coefficients; this makes it also suitable for smoothing. Convergence results and good choices for the constant \(c\) in the multiquadric radial basis function \(\phi(r)=\sqrt{r^2+c^2}\) are also addressed.