Low-Rank Matrix Approximation and Subspace Tracking

Patrick Dewilde and Alle-Jan van der Veen
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Patrick Dewilde: Delft University of Technology, DIMES
Alle-Jan van der Veen: Delft University of Technology, DIMES

Chapter 11 in Time-Varying Systems and Computations, 1998, pp 307-333 from Springer

Abstract: Abstract The usual way to compute a low-rank approximant of a matrix H is to take its singular value decomposition (SVD) and truncate it by setting the small singular values equal to 0. However, the SVD is computationally expensive. Using the Hankel-norm model reduction techniques in chapter 10, we can devise a much simpler generalized Schurtype algorithm to compute similar low-rank approximants. Since rank approximation plays an important role in many linear algebra applications, we devote an independent chapter to this topic, even though this leads to some overlap with previous chapters.

Keywords: Singular Value Decomposition; Elementary Rotation; Subspace Estimate; Subspace Tracking; Principal Subspace (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4757-2817-0_11

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