On the minimal derivative oscillation for deficient quartic splines of Marsden’s type

Abstract

In this note we investigate the possibility to minimize the derivative oscillation for deficient quartic splines of Marsden’s type, motivated by the purpose to reduce the excessive oscillations near midpoints. The error estimate of the obtained quartic spline interpolant is derived considering a comparison with the cases of the smooth quartic spline having continuous second derivative and the quartic spline that has minimal Euclidean norm of the second derivative.