Abstract
In this paper, we consider the problem of constructing smoothing spline curves recursively each time when a new set of data is observed. The spline curves are constituted by employing normalized uniform B-splines as the basis functions. Then, based on the basic problem of optimal smoothing splines and an idea of recursive least squares method, a recursive design algorithm of optimal smoothing splines is developed. Assuming that the data for smoothing is obtained by sampling curve, we analyze asymptotical and statistical properties of smoothing spline curve when the number of iterations tends to infinity. The algorithm and analyses are extended to the case of periodic splines. We demonstrate the effectiveness and usefulness by numerical examples.
