Statistical regularization of systems of algebraic equations

Abstract

THE QUESTION of the construction of the pseudo solution of the linear algebraic system Az = u, is considered when the vector u is not known exactly but experimental realization of it with a normally distributed error and covariance matrix σσ T are known. The method of solution used is the method of filtering of Markov processes. In the case where the error of the vector u is distributed arbitrarily, using the regularization method of A. N. Tikhonov [1], we present a filter of the solution of this problem.