Fast Low-Rank Modifications of the Thin Singular Value Decomposition

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 × q matrix can be computed in O(pqr) time for r √ min(p, q). © 2005 Elsevier Inc. All rights reserved. AMS classification: 49M27; 15A18; 15A23; 65F20