Periodic smoothing splines

Periodic smoothing splines appear for example as generators of closed, planar curves, and in this paper they are constructed using a controlled two point boundary value problem in order to generate the desired spline function. The procedure is based on minimum norm problems in Hilbert spaces and a suitable Hilbert space is defined together with a corresponding linear affine variety that captures the constraints. The optimization is then reduced to the computationally stable problem of finding the point in the constraint variety closest to the data points. Key words: spline smoothing; periodic; two-point boundary value problem; constrained optimization

• Type: Journal
• Year: 2008
• Where: AUTOMATICA
• Authors: Hiroyuki Kano, Magnus Egerstedt, Hiroyuki Fujioka, Satoru Takahashi, Clyde F. Martin
• Keywords: AUTOMATICA 2008, Boundary Value Problem, Hilbert Space, Periodic Smoothing Splines