L-Spline Interpolation for Differential Operators of Order 4 with Constant Coefficients

In this paper it is shown that many features from polynomial spline methods used in nonparametric regression and smoothing procedures carry over to the class of L-splines where L is a linear differential operator of order 4 with constant coefficients. Special attention is given to the question whether an analogue of the Reinsch algorithm is valid and criteria are given such that the associated matrix R is strictly diagonal dominant.Project KP-06-N32-8; Project KP-06N42-2 with Bulgarian NSF; Grant No BG05M2OP001-1.001-0003,financed by the Science and Education for Smart Growth Operational Program (2014-2020) and co-financed by the European Union through the European structural and Investment funds