Fast algorithms for interpolation with L-splines for differential operators [formula omitted] of order 4 with constant coefficients

Abstract

In the classical theory of cubic interpolation splines there exists an algorithm which works with only On arithmetic operations. Also, the smoothing cubic splines may be computed via the algorithm of Reinsch which reduces their computation to interpolation cubic splines and also performs with On arithmetic operations. In this paper it is shown that many features of the polynomial cubic spline setting carry over to the larger class of L-splines where L is a linear differential operator of order 4 with constant coefficients. Criteria are given such that the associated matrix R is strictly diagonally dominant which implies the existence of a fast algorithm for interpolation. We provide an example of two L-splines interpolating S&P500 data.