Optimal properties for deficient quartic splines of Marsden type

In this work, we obtain an improved error estimate in the interpolation with the Hermite $C^{2}$-smooth deficient complete quartic spline that has the distribution of nodes following the Marsden type scheme and investigate the possibilities to compute the derivatives on the knots such that the obtained spline $S\in C^{1}[a,b]$ has minimal curvature and minimal $L^{2}$-norm of $S^{\prime }$ and $S^{\prime \prime \prime }$. In each case, the interpolation error estimate is performed in terms of the modulus of continuity.%MCEPASTEBIN