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Zap. Nauchn. Sem. POMI, 2006, Volume 334, Pages 193–211 (Mi znsl232)  

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

A. O. Rodnikov, B. A. Samokish

Saint-Petersburg State University

Abstract: 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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English version:
Journal of Mathematical Sciences (New York), 2007, 141:6, 1678–1689

Bibliographic databases:

UDC: 518.512.25
Received: 14.09.2006

Citation: A. O. Rodnikov, B. A. Samokish, “An estimate of the round-off error in the elimination problem”, Computational methods and algorithms. Part XIX, Zap. Nauchn. Sem. POMI, 334, POMI, St. Petersburg, 2006, 193–211; J. Math. Sci. (N. Y.), 141:6 (2007), 1678–1689

Citation in format AMSBIB
\Bibitem{RodSam06}
\by A.~O.~Rodnikov, B.~A.~Samokish
\paper An estimate of the round-off error in the elimination problem
\inbook Computational methods and algorithms. Part~XIX
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 334
\pages 193--211
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl232}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2270917}
\zmath{https://zbmath.org/?q=an:1120.65060}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 141
\issue 6
\pages 1678--1689
\crossref{https://doi.org/10.1007/s10958-007-0078-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33847004801}


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