ESTIMATES OF THE SOLUTIONS OF OPERATOR EQUATIONS UNDER UNCERTAINTY
Oleksandr Nakonechnyi, P. M. Zinko, T. P. Zinko · Kibernetyka ta Systemnyi Analiz · 2024
The paper focuses on finding the guaranteed estimates for rectangular matrices that satisfy the linear operator equations with unknown right-hand sides. Under certain assumptions, it is shown that guaranteed estimates of matrices can be found as the solutions of systems of operator equations. In the case where observation data are given with deterministic errors, which belong to certain bounded sets, we obtain the expressions for upper and lower estimates of the solutions of such equations, as well as expressions for upper and lower errors of such estimates. The obtained results are illustrated by an example. Keywords: linear operator equation, operator core, conjugate operator, guaranteed a posteriori estimate of matrix, guaranteed a posteriori error of the estimate of matrix, minimum by norm solution of the equation.