On Some Methods of the Construction of Smoothing Splines

Abstract

This chapter discusses the methods of the construction of smoothing splines. The algorithm or experimental data smoothing using the cubic spline with an a priori chosen extent of smoothing and its modifications became, at the beginning of the last decade, the most widely used algorithms for curve fitting. The smoothing B-spline represents the other often used group of smoothing algorithms, where it is necessary to choose the extent of smoothing explicitly. It is proposed to construct interpolating and smoothing splines via reproducing kernel techniques. In this approach was exploited in constructing smoothing splines in such a way that the extent of smoothing was automatically determined by minimizing the general cross-validation. The chapter deals with a new method of the smoothing spline construction.