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The Canonical Correlations of Matrix Pairs and their Numerical Computation

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Linear Algebra for Signal Processing

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 69))

Abstract

This paper is concerned with the analysis of canonical correlations of matrix pairs and their numerical computation. We first develop a decomposition theorem for matrix pairs having the same number of rows which explicitly exhibits the canonical correlations. We then present a perturbation analysis of the canonical correlations, which compares favorably with the classical first order perturbation analysis. Then we propose several numerical algorithms for computing the canonical correlations of general matrix pairs; emphasis is placed on the case of large sparse or structured matrices.

This work was supported in part by NSF grant DRC-8412314 and Army contract DAAL-03-90-G-0105

This work was supported in part by Army contract DAAL-03-90-G-0105

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Author information

Author notes

  1. Hongyuan Zha

    Present address: Dept. of Computer Science and Engineering, 307 Pond Laboratory, The Pennsylvania State University, University Park, PA, 16802-6103, USA

Authors and Affiliations

  1. Computer Science Department, Stanford University, Stanford, CA, 94305-2140, USA

    Gene H. Golub

  2. Scientific Computing & Computational Mathematics, Stanford University, Stanford, CA, 94305-2140, USA

    Hongyuan Zha

Authors
  1. Gene H. Golub
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  2. Hongyuan Zha
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Editor information

Editors and Affiliations

  1. School of Electrical Engineering 337 E&TC, Cornell University, Ithaca, NY, 14853-3801, USA

    Adam Bojanczyk

  2. Dartmouth College, Thayer School of Engineering, Hanover, NH, 03755-8000, USA

    George Cybenko

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© 1995 Springer-Verlag New York, Inc.

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Golub, G.H., Zha, H. (1995). The Canonical Correlations of Matrix Pairs and their Numerical Computation. In: Bojanczyk, A., Cybenko, G. (eds) Linear Algebra for Signal Processing. The IMA Volumes in Mathematics and its Applications, vol 69. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4228-4_3

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  • DOI: https://doi.org/10.1007/978-1-4612-4228-4_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8703-2

  • Online ISBN: 978-1-4612-4228-4

  • eBook Packages: Springer Book Archive

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