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On the condition numbers associated with the polar factorization of a matrix
- Source :
- Numerical Linear Algebra with Applications. 7:337-354
- Publication Year :
- 2000
- Publisher :
- Wiley, 2000.
-
Abstract
- We are interested in the calculation of explicit formulae for the condition numbers of the two factors of the polar decomposition of a full rank real or complex m × n matrix A, where m ≥ n. We use a unified presentation that enables us to compute such condition numbers in the Frobenius norm, in cases where A is a square or a rectangular matrix subjected to real or complex perturbations. We denote by σ1 (respectively σn) the largest (respectively smallest) singular value of A, and by K(A) = σ1/σn the generalized condition number of A. Our main results are that the absolute condition number of the Hermitian polar factor is √2(1 + K(A)2)1/2/(1 + K(A)) and that the absolute condition number of the unitary factor of a rectangular matrix is 1/σn. Copyright © 2000 John Wiley & Sons, Ltd.
Details
- ISSN :
- 10991506 and 10705325
- Volume :
- 7
- Database :
- OpenAIRE
- Journal :
- Numerical Linear Algebra with Applications
- Accession number :
- edsair.doi...........e2a459a0cf416f180bcf4fc9ae8a7e88