Modifiable low‐rank approximation to a matrix |
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Authors: | Jesse L. Barlow Hasan Erbay |
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Affiliation: | 1. Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA 16802‐6106, U.S.A.;2. Department of Computer Engineering, K?r?kkale University, Yah?ihan, K?r?kkale, Turkey 71451, Turkey |
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Abstract: | A truncated ULV decomposition (TULVD) of an m×n matrix X of rank k is a decomposition of the form X = ULVT+E, where U and V are left orthogonal matrices, L is a k×k non‐singular lower triangular matrix, and E is an error matrix. Only U,V, L, and ∥E∥F are stored, but E is not stored. We propose algorithms for updating and downdating the TULVD. To construct these modification algorithms, we also use a refinement algorithm based upon that in (SIAM J. Matrix Anal. Appl. 2005; 27 (1):198–211) that reduces ∥E∥F, detects rank degeneracy, corrects it, and sharpens the approximation. Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | orthogonal decomposition rank estimation subspace estimation |
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