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Inversion of Generalized Cauchy Matrices and other Classes of Structured Matrices

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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

Fast inversion algorithms for strongly nonsingular matrices of the form \(C = \left[ {\frac{{z_i^T{y_j}}}{{{c_i} - {d_j}}}} \right]\) (generalized Cauchy matrices), where z i , y j are column vectors and c i , d j are complex numbers, are presented. The approach is based on the interpretation of equations Cξ = η as tangential interpolation problems. Furthermore, it is described how other types of structured matrices like Toeplitz matrices and their generalizations can be transformed into generalized Cauchy matrices. This transformation can be utilized in order to get stable algorithms.

The work was carried out during a visit at the IMA, University of Minnesota in Minneapolis, March 1992.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait

    Georg Heinig

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  1. Georg Heinig
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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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Heinig, G. (1995). Inversion of Generalized Cauchy Matrices and other Classes of Structured Matrices. 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_5

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  • DOI: https://doi.org/10.1007/978-1-4612-4228-4_5

  • 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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