Condition numbers of random triangular matrices

SIAM Journal on Matrix Analysis and Applications

Volumn 19, Issue 2, 1998, Pages 564-581

  Viswanath, D ^a   Trefethen, L N ^b  

^a Department of Computer Science and School of Operations Research and Information Engineering   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Exponentially nonnormal matrices; Matrix condition numbers; Random triangular matrices; Strong limit theorems

Indexed keywords

EID: 0032394355     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479896312869     Document Type: Article

References (22)

1. M. ABRAMOWITZ AND I.A. STEGUN, EDS., Handbook of Mathematical Functions, Dover, New York, 1970.
2. P. BILLINGSLEY, Probability and Measure, 2nd ed., John Wiley, New York, 1986.
3. J. B. CONWAY, Functions of One Complex Variable, Springer, New York, 1995.
4. A. EDELMAN, Eigenvalues and Condition Numbers of Random Matrices, Ph.D. dissertation and Numerical Analysis Report 89-7, Massachusetts Institute of Technology, Cambridge, MA, 1989.
5. A. EDELMAN, Eigenvalues and condition numbers of random matrices, SIAM J. Matrix Anal. Appl., 9 (1988), pp. 543-560.
6. W. FELLER, An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd ed., John Wiley, New York, 1971.
7. L. V. FOSTER, Gaussian elimination with partial pivoting can fail in practice, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1354-1362.
8. I. S. GRADSHTEYN AND I. W. RYZHIK, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965.
9. H. H. GOLDSTINE AND J. VON NEUMANN, Numerical inverting of matrices of high order, Amer. Math. Soc. Bull., 53 (1947), pp. 1021-1099.
10. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1996.
11. A. K. GUPTA AND Z. GOVINDARAJULU, Distribution of the quotient of two independent Hotelling T2-variates, Comm. Statist., 4 (1975), pp. 449-453.
12. N. J. HIGHAM, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, PA, 1996.
13. G. HARDY, J. E. LITTLEWOOD, AND G. POLYA, Inequalities, 2nd ed., Cambridge University Press, Cambridge, UK, 1988.
14. H. HOTELLING, Some new methods in matrix calculation, Ann. Math. Statist., 14 (1943), pp. 1-34.
15. M. L. MEHTA, Random Matrices and the Statistical Theory of Energy Levels, Academic Press, New York, 1967.
16. J. W. SILVERSTEIN, The smallest eigenvalue of a large-dimensional Wishart matrix, Ann. Probab., 13 (1985), pp. 1364-1368.
17. L. N. TREFETHEN AND D. BAU, III, Numerical Linear Algebra, SIAM, Philadelphia, PA, 1997.
18. L. N. TREFETHEN AND R. S. SCHREIBER, Average-case stability of Gaussian elimination, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 335-360.
19. J. H. WILKINSON, Error Analysis of direct methods of matrix inversion, J. Assoc. Comput. Mach., 8 (1961), pp. 281-330.
20. S. J. WRIGHT, A collection of problems for which Gaussian elimination with partial pivoting is unstable, SIAM J. Sci. Comput., 14 (1993), pp. 231-238.
21. D. VISWANATH, Random Fibonacci sequences and the number 1.13198824 . . . , Math. Comp., submitted.
22. M. C. YEUNG AND T. F. CHAN, Probabilistic analysis of Gaussian elimination without pivoting, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 499-517.