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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Low rank update of singular values


Authors: Delin Chu and Moody Chu
Journal: Math. Comp. 75 (2006), 1351-1366
MSC (2000): Primary 68F18, 93B55, 15A18
Published electronically: February 27, 2006
MathSciNet review: 2219032
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Abstract: The notion of a low rank update arises in many important applications. This paper deals with the inverse problem of updating a rectangular matrix by additive low rank matrices so as to reposition the associated singular values. The setting is analogous to the classical pole assignment problem where eigenvalues of a square matrix are relocated. Precise and easy-to-check necessary and sufficient conditions under which the problem is solvable are completely characterized, generalizing some traditional Weyl inequalities for singular values. The constructive proof makes it possible to compute such a solution numerically. A pseudo algorithm is outlined.


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Additional Information

Delin Chu
Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
Email: matchudl@math.nus.edu.sg

Moody Chu
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
Email: chu@math.ncsu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01825-4
PII: S 0025-5718(06)01825-4
Keywords: Singular values, low rank update, interlacing properties, pole assignment.
Received by editor(s): December 17, 2004
Received by editor(s) in revised form: April 1, 2005
Published electronically: February 27, 2006
Additional Notes: This research was supported in part by the National Science Foundation under grants DMS-0073056 and CCR-0204157
Article copyright: © Copyright 2006 American Mathematical Society