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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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: 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 $ {\kappa _D}(A) = {\left\Vert A \right\Vert _F} \bullet \left\Vert {{A^{ - 1}}} \right\Vert$. 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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Keywords: Condition number, ill-conditioning, multivariate statistics, numerical analysis, random matrix
Article copyright: © Copyright 1992 American Mathematical Society