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%
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.