Tails of condition number distributions

SIAM Journal on Matrix Analysis and Applications

Volumn 27, Issue 2, 2006, Pages 547-560

  Edelman, Alan ^a   Sutton, Brian D ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Condition number; Random matrix; Wishart

Indexed keywords

CONDITION NUMBER; RANDOM MATRIX; WISHART;

ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; ESTIMATION; RANDOM NUMBER GENERATION;

MATRIX ALGEBRA;

EID: 33646242497     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/040614256     Document Type: Article

References (13)

1. J.-M. AZAÏS AND M. WSCHEBOR, Upper and lower bounds for the tails of the distribution of the condition number of a Gaussian matrix, SIAM J. Matrix Anal. Appl., 26 (2005). pp. 426-440.
2. J. W. DEMMEL, The probability that a numerical analysis problem is difficult, Math. Comp., 50 (1988), pp. 449-480.
3. I. DUMITRIU, Eigenvalue Statistics for Beta-Ensembles, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 2003.
4. I. DUMITRIU AND A. EDELMAN, Matrix models for beta ensembles, J. Math. Phys., 43 (2002), pp. 5830-5847.
5. A. EDELMAN, Eigenvalues and Condition Numbers of Random Matrices, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1989.
6. I. M. JOHNSTONE, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist., 29 (2001), pp. 295-327.
7. P. KOEV AND A. EDELMAN, Efficient evaluation of the hypergeometric function of matrix argument, Math. Comp., submitted.
8. R. J. MUIRHEAD, Aspects of Multivariate Statistical Theory, Wiley Series Probab. Math. Statist., John Wiley & Sons, New York, 1982.
9. P.-O. PERSSON, Numerical Methods for Eigenvalue Distributions of Random Matrices, http://arxiv.org/abs/math-ph/0501068 (19 March 2005).
10. J. W. SlLVERSTElN, The smallest eigenvalue of a large-dimensional Wishart matrix, Ann. Probab., 13 (1985), pp. 1364-1368.
11. S. SMALE, On the efficiency of algorithms of analysis, Bull. Amer. Math. Soc. (N.S.), 13 (1985). pp. 87-121.
12. C. A. TRACY AND H. WIDOM, Airy kernel and Painlevé II, in Isomonodromic Deformations and Applications in Physics (Montréal, QC, 2000), CRM Proc. Lect. Notes 31, J. Harnad and A. Its, eds., American Mathematical Society, Providence, RI, 2002, pp. 85-96.
13. J. VON NEUMANN, Collected Works, Vol. V: Design of Computers, Theory of Automata and Numerical Analysis, A Pergamon Press Book, Macmillan, New York, 1963.