On the distribution of a scaled condition number
Author:
Alan Edelman
Journal:
Math. Comp. 58 (1992), 185190
MSC:
Primary 15A52; Secondary 15A12, 62H10, 65F99, 65U05
MathSciNet review:
1106966
Fulltext PDF Free Access
Abstract 
References 
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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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 M. Abramowitz and I. A. Stegun, eds., Handbook of mathematical functions, Dover, New York, 1970.
 [2]
 T. W. Anderson, An introduction to multivariate statistical analysis, Wiley, New York, 1958. MR 0091588 (19:992a)
 [3]
 A. W. Davis, On the ratios of the individual latent roots to the trace of a Wishart matrix, J. Multivariate Anal. 2 (1972), 440443. MR 0324834 (48:3183)
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 , Eigenvalues and condition numbers of random matrices, Ph.D. thesis, Dept. of Math., M.I.T., 1989.
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 P. R. Krishnaiah and F. J. Schuurmann, On the evaluation of some distributions that arise in simultaneous tests for the equality of the latent roots of the covariance matrix, J. Multivariate Anal. 4 (1974), 265282. MR 0359178 (50:11633)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199211069662
PII:
S 00255718(1992)11069662
Keywords:
Condition number,
illconditioning,
multivariate statistics,
numerical analysis,
random matrix
Article copyright:
© Copyright 1992 American Mathematical Society
