Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices

Details Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices

2003-10-12

arxiv.org/abs/cs/0310022v4

Computer Science

Numerical Analysis

corrected some minor mistakes

Scientific paper

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).

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