Geodesic
An estimate of the round-off error in the elimination problem
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 193-211 
A. O. Rodnikov; B. A. Samokish. An estimate of the round-off error in the elimination problem. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 193-211. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a13/
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     title = {An estimate of the round-off error in the elimination problem},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a13/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

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