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- W2952318043 abstract "Let $orig{A}$ be any matrix and let $A$ be a slight random perturbation of $orig{A}$. We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the smoothed precision needed by Gaussian elimination without pivoting. Our results improve the average-case analysis of Gaussian elimination without pivoting performed by Yeung and Chan (SIAM J. Matrix Anal. Appl., 1997)." @default.
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- W2952318043 date "2003-10-12" @default.
- W2952318043 modified "2023-09-27" @default.
- W2952318043 title "Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices" @default.
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