Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
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
Full-text PDF Free Access

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 $ {\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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 15A52, 15A12, 62H10, 65F99, 65U05

Retrieve articles in all journals with MSC: 15A52, 15A12, 62H10, 65F99, 65U05


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1106966-2
PII: S 0025-5718(1992)1106966-2
Keywords: Condition number, ill-conditioning, multivariate statistics, numerical analysis, random matrix
Article copyright: © Copyright 1992 American Mathematical Society