Quasilinear Interpolation by Minimal Splines

The paper studies quasilinear interpolation by minimal splines constructed on nonuniform grids with multiple nodes. Asymptotic representations for normalized splines are obtained. The sharpness of biorthogonal approximation and the order of accuracy of quasilinear interpolation with respect to the grid stepsize are established. Results of numerical experiments on approximating some test functions, which demonstrate the effect of choosing a generating vector function in constructing the corresponding minimal spline, are presented.