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Low-Rank Matrix Approximation and Subspace Tracking

In: Time-Varying Systems and Computations

Author

Listed:
  • Patrick Dewilde

    (Delft University of Technology, DIMES)

  • Alle-Jan van der Veen

    (Delft University of Technology, DIMES)

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.

Suggested Citation

  • Patrick Dewilde & Alle-Jan van der Veen, 1998. "Low-Rank Matrix Approximation and Subspace Tracking," Springer Books, in: Time-Varying Systems and Computations, chapter 11, pages 307-333, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-2817-0_11
    DOI: 10.1007/978-1-4757-2817-0_11
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