Twelfth degree spline with application to quadrature

Abstract

In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applicability and efficiency of the new method.

On construction of a new interpolation tool: cubic $q$-spline

“…Despite the popularity of B-spline, new generalizations of spline continue to appear. Some of them concerns about preserving of convexity [12], some of them about smoothness of interpolation [13], and others about degrees of freedom [14]. Classical cubic spline already proved itself in data and curve fitting problems.…”