### Abstract

In signal processing, the singular value decomposition and rank characterization of matrices play prominent roles. The mapping which associates with any complex m x 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 σ is sufficiently close to αP+ I,. 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 [l]).

Original language | English (US) |
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Pages (from-to) | 1211-1212 |

Number of pages | 2 |

Journal | IEEE Transactions on Acoustics, Speech, and Signal Processing |

Volume | 35 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1987 |

### ASJC Scopus subject areas

- Signal Processing

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## Cite this

*IEEE Transactions on Acoustics, Speech, and Signal Processing*,

*35*(8), 1211-1212. https://doi.org/10.1109/TASSP.1987.1165262