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

The paper demonstrates that in computing a linear form $(g,x)$ of the solution of a system of linear equations $Ax=f$, the round-off error depends on the quantities $\|A^{-1}f\|$ and $\|A^{T^{-1}}g\|$ 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.