Monotone Smoothing Spline Curves Using Normalized Uniform Cubic B-splines

Abstract

This paper considers a problem on the non-negative derivative constraints on the cubic smoothing spline curves using normalized uniform B-splines as the basis functions. In particular, we derive a condition for monotonic constraints over interval along the line of Fritsch and Carlon's works in [1]. Moreover, we present how these results are incorporated in the optimal smoothing spline problems. The performance is examined by some numerical examples.