CONTINUITY OF CLOSEST RANK-P APPROXIMATIONS TO MATRICES.

Hans Mittelmann, James A. Cadzow

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In signal processing, the singular value decomposition and rank characterization of matrices play prominent roles. The mapping which associates with any complex m multiplied by n matrix X its closest rank-p approximation X**(**p**) need not be continuous. When the pth and the (p plus 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 sigma //p is sufficiently close to sigma //p // plus //1. It is finally shown that this mapping is closed in the sense of W. I. Zangwill (1969). The property of closedness is an essential assumption of a global convergence proof for algorithms inolving this mapping.

Original languageEnglish (US)
Pages (from-to)1211-1212
Number of pages2
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
VolumeASSP-35
Issue number8
StatePublished - Aug 1987

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Singular value decomposition
Signal processing

ASJC Scopus subject areas

  • Signal Processing

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CONTINUITY OF CLOSEST RANK-P APPROXIMATIONS TO MATRICES. / Mittelmann, Hans; Cadzow, James A.

In: IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-35, No. 8, 08.1987, p. 1211-1212.

Research output: Contribution to journalArticle

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