Componentwise Condition Numbers of Random Sparse Matrices

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2009Embargo end date: 01 Jan 2008 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Matrix Analysis and Applications, volume 31, pages 721-731 (issn: 0895-4798, eissn: 1095-7162,

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Authors: Dennis Cheung; Felipe Cucker;

doi: 10.1137/080729463 , 10.48550/arxiv.0807.0956

arXiv: 0807.0956

Componentwise Condition Numbers of Random Sparse Matrices

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Abstract

We prove an O(log n) bound for the expected value of the logarithm of the componentwise (and, a fortiori, the mixed) condition number of a random sparse n x n matrix. As a consequence, small bounds on the average loss of accuracy for triangular linear systems follow.

Keywords

Probability (math.PR), FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Mathematics - Probability, 15A12, 15A52

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