параметр регуляризації

Three different principles were considered for the determination of the regulanzation parameter in the variational problem of data processing. These principles are based exclusively on properties of the covariance matrixes and they are treated as analogies of traditional principles of misclosure, quasisolution and smoothing functional, respectively. It is remarkable, that the classical case of the least squares collocation (with the regulanzation parameter equal to 1) was obtained as one of the roots of the equation corresponding to the misclosure principle.

The regulanzation algorithm was developed on the basis of such Jit of the normal operator which is closed to a system of linear equations with scalar or unit matrix. The application of the famous theorem on the spectral expansion of normal matrixes Jed to introducing of the simplest matrix norm (connected with the traditional Euclidean norm) and allowed form special condition, which provides the determination of the regulanzation parameter.