Splines and Linear Control Theory

Abstract

In this work, the relationship between splines and the linear control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.