Error estimates in solving linear systems

Given a linear system A_x=b, with a real square nonsingular coefficient matrix, the error on the solution x is studied with respect to data perturbations and rounding errors of the computation. Assuming local errors to be independent random variables, the expected value of the total error is computed as a function of x, say e(x). The mean of e(x) in the unitary ball is then computed, obtaining statistical estimates to the errors. Moreover, the influence of diagonal scaling on the stability of the computation is studied. These results are applied to the solution of triangular systems, to Gaussian elimination and orthogonalization techniques.