In the paper estimation problem for solution of linear algebraic equations with unknown right-sides part represented by determined or stochastic vector is considered. The realization of random vector linearly connected to these solutions is observed. The definitions of linear mean-square guaranteed estimate and linear guaranteed mean-square error for solutions of linear equations are proposed. In case of restrictions on unknown parameters and correlation matrixes the representation of these estimates via solutions of some nonlinear equations are obtained. The guaranteed estimation problem of linear function on solutions of linear algebraic equations is also studied. This paper shows, that guaranteed estimates of functions and guaranteed errors are linearly depended on solutions of systems of linear equations. In case of growing number of observations the convergence problem of guaranteed estimates is also considered. Obtained results are applied for estimation problem of periodic solutions of 2-orderdiscrete time linear equation with unknown parameters.
Дослiджуються питанння пов"язанi з лiнiйними середньоквадратичними оцiнками розв"язкiв лiнiйних алгебраїчних рiвнянь. Показано, що гарантованi оцiнки при спецiальних обмеженнях на розв"язки таких рiвнянь та похибки спостережень виражаються через розв"язки матричних та лiнiйних алгебраїчних рiвнянь.
