Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 415, Issue 1, Pages 20-30Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2005.07.021
Keywords
singular value decomposition; sequential updating; subspace tracking
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This paper develops an identity for additive modifications of a singular value decomposition (SVD) to reflect updates, downdates, shifts, and edits of the data matrix. This sets the stage for fast and memory-efficient sequential algorithms for tracking singular values and subspaces. In conjunction with a fast solution for the pseudo-inverse of a submatrix of an orthogonal matrix, we develop a scheme for computing a thin SVD of streaming data in a single pass with linear time complexity: A rank-r thin SVD of a p x q matrix can be computed in O(pqr) time for r <= root min(p,q). (c) 2005 Elsevier Inc. All rights reserved.
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