By Topic

Continuity of closest rank-p approximations to matrices

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Mittelmann, H. ; Arizona State University, Tempe, AZ ; Cadzow, James A.

In signal processing, the singular value decomposition and rank characterization of matrices play prominent roles. The mapping which associates with any complex m × n matrix X its closest rank-p approximation X(p)need not be continuous. When the pth and the (p + 1)st singular values of X are equal, this mapping maps, in fact, a matrix to a set of matrices. Furthermore, an example is given to show that large errors in computing X(p)can be expected when σpis sufficiently close to σp+1. It is finally shown that this mapping is closed in the sense of Zangwill. The property of closedness is an essential assumption of a global convergence proof for algorithms involving this mapping (e.g., see [1]).

Published in:

Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:35 ,  Issue: 8 )