SUMMARYThis paper presents a formulation of a cubic spline that fits the first derivatives of a function at mesh points and the function value and its second derivative at the beginning of the interval. Error bounds for the function and its first three derivatives are derived over the whole interval. This formulation can be applied, in particular, to quadratures.
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.