On the distribution of a scaled condition number

Author:
Alan Edelman

Journal:
Math. Comp. **58** (1992), 185-190

MSC:
Primary 15A52; Secondary 15A12, 62H10, 65F99, 65U05

MathSciNet review:
1106966

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we give the exact distribution of a scaled condition number used by Demmel to model the probability that matrix inversion is difficult. Specifically, consider a random matrix *A* and the scaled condition number . Demmel provided bounds for the condition number distribution when *A* has real or complex normally distributed elements. Here, we give the exact formula.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1992-1106966-2

Keywords:
Condition number,
ill-conditioning,
multivariate statistics,
numerical analysis,
random matrix

Article copyright:
© Copyright 1992
American Mathematical Society