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

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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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     author = {A. O. Rodnikov and B. A. Samokish},
     title = {An estimate of the round-off error in the elimination problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
     volume = {334},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a13/}
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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/