๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Some remarks on the condition number of a real random square matrix

โœ Scribed by J.A. Cuesta-Albertos; M. Wschebor


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
135 KB
Volume
19
Category
Article
ISSN
0885-064X

No coin nor oath required. For personal study only.

โœฆ Synopsis


In this paper we obtain some bounds for the expectation of the logarithm of the condition number of a random matrix whose elements are independent and identically distributed random variables. We also include some examples and extensions to cover the smoothed analysis as well as higher order moments.


๐Ÿ“œ SIMILAR VOLUMES


The distribution of the maximum conditio
โœ Debra Lewis; Mike Shub ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 92 KB

If P A (ฯ‡) denotes the probability that the maximum condition number along a great circle passing through a matrix A in the unit sphere in the space of 2 ร— 2 matrices is less than ฯ‡, then P A (ฯ‡) always attains its maximum at the normalized identity matrix. This result is the first nontrivial case o

Effect of small rank modification on the
โœ Xinmao Wang ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 422 KB

The condition number of a matrix plays an important role in numerical matrix computations. In this paper, we investigate how much the small rank modification method can reduce the condition number of a matrix.