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Approximation with Kronecker Products

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Linear Algebra for Large Scale and Real-Time Applications

Part of the book series: NATO ASI Series ((NSSE,volume 232))

Abstract

Let A be an m-by-n matrix with m = m 1 m 2 and n = n 1 n 2. We consider the problem of finding \(B \in {\mathbb{R}^{{m_1} \times {n_1}}}\;and\;C\; \in \;{\mathbb{R}^{{m_2} \times {n_2}}}\;so\;that\;||\;A - B \otimes C\;||{\;_F}\) is minimized. This problem can be solved by computing the largest singular value and associated singular vectors of a permuted version of A. If A is symmetric, definite, non-negative, or banded, then the minimizing B and C are similarly structured. The idea of using Kronecker product preconditioned is briefly discussed.

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Authors and Affiliations

  1. Department of Computer Science, Cornell University, Ithaca, New York, 14853, USA

    C. F. Van Loan & N. Pitsianis

Authors
  1. C. F. Van Loan
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  2. N. Pitsianis
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Editors and Affiliations

  1. ESAT Laboratory, Katholieke Universiteit Leuven, Leuven, Belgium

    Marc S. Moonen  & Bart L. R. De Moor  & 

  2. Computer Science Department, Stanford University, Stanford, California, USA

    Gene H. Golub

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© 1993 Springer Science+Business Media Dordrecht

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Van Loan, C.F., Pitsianis, N. (1993). Approximation with Kronecker Products. In: Moonen, M.S., Golub, G.H., De Moor, B.L.R. (eds) Linear Algebra for Large Scale and Real-Time Applications. NATO ASI Series, vol 232. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8196-7_17

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  • DOI: https://doi.org/10.1007/978-94-015-8196-7_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4246-0

  • Online ISBN: 978-94-015-8196-7

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