Some remarks on the condition number of a real random square matrix
โ 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
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โฆ 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.
๐ SIMILAR VOLUMES
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
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.