An estimate for the round-off error in the elimination problem

The paper demonstrates that in computing a linear form (g, x) on the solution of a system of linear equations Ax = f, the round-off error depends on the quantities ‖A⁻¹f‖ and ‖A^T−1g‖ rather than on the condition number of the coefficient matrix A. Estimates of the inherent and round-off errors in solving the above problem by the orthogonalization method are provided. Numerical results confirming theoretical conclusions are presented. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 193–211.