Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides

In the spirit of Wilkinson's [1, 2] backward error analysis, conditions are established under which a given approximate solution of a system of n linear equations with n unknowns is the exact solution of a modified system whose coefficients and right-hand sides are within a given neighborhood of those of the original system. © 1964 Springer-Verlag.