On the structure of closeness estimates for pseudosolutions of initial and perturbed systems of linear algebraic equations

An example of an initial and a perturbed system of linear algebraic equations is considered, in which the perturbation matrix (regarded as a parameter) lies in the domain where the pseudosolution depends continuously on the perturbation matrix. However, the application of Godunov's well-known estimate to the considered example reveals that the requirement for the continuous dependence of the pseudosolution on the perturbation matrix is violated. The present study was motivated by this contradiction and was aimed at its resolution. Estimates for the closeness between the pseudosolutions of the original and perturbed systems are obtained for which the domain of continuous dependence of the pseudosolution on the perturbation matrix is larger. A comparison of these estimates with those of Lawson and Hanson shows that they are no worse than the latter.