The paper contains short description of -algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. Some realizations of this algorithm based on the continuous and discrete splines are presented here. Few examples concerning with compression in the solving of approximation problems and colour image processing are described and discussed.
The paper presents an alternative approach to the design of a hybrid adaptive controller of Linear Quadratic Gaussian (LQG) type for linear stochastic controlled system. The approach is based on the combination standard building blocks of discrete LQG adaptive controller with the non-standard technique of modelling of a controlled system and spline approximation of involved signals. The method could be of interest for control of systems with complex models, in particular distributed parameter systems....
Two universally applicable smoothing operations adjustable to meet the specific properties of the given smoothing problem are widely used: 1. Smoothing splines and 2. Smoothing digital convolution filters. The first operation is related to the data vector with respect to the operations , and to the smoothing parameter . The resulting function is denoted by . The measured sample is defined on an equally spaced mesh