抄録
We consider a problem of designing optimal smoothing spline curves by employing an approach based on linear control systems. In particular, we establish a design method of multi-level smoothing splines, a smoothing counterpart of Hermite interpolations, assuming that not only function values but also its derivatives are available as the data. The problem is formulated as an optimal control problem, and a necessary and sufficient condition for the existence of unique optimal solution is derived. The computational algorithm is simple as well as feasible numerically, and its effectiveness is verified by numerical examples.
