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Randomized Acceleration of Fundamental Matrix Computations

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STACS 2002 (STACS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

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Abstract

We accentuate the power of several known effective methods by combining them together and adding some novel techniques. As a result, we substantially improve the known record randomized bitoperation complexity estimates for various fundamental computations with integer matrices. This includes the computation of the determinant, minimum and characteristic polynomials, Smith and Frobenius invariant factors, and the eigenvalues. Most of the algorithms can be further accelerated where the input matrix can be multiplied by a vector fast, they can be effectively parallelized and extended to matrix polynomials.

Supported by NSF Grant CCR 9732206 and PSC CUNY Awards 61393-0030, 62435- 0031, and 66383-0032

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Lehman College of CUNY, 10468, Bronx, NY, USA

    Victor Y. Pan

Authors
  1. Victor Y. Pan
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

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© 2002 Springer-Verlag Berlin Heidelberg

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Pan, V.Y. (2002). Randomized Acceleration of Fundamental Matrix Computations. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_17

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  • DOI: https://doi.org/10.1007/3-540-45841-7_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

  • eBook Packages: Springer Book Archive

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