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I/O Efficient Algorithms for Block Hessenberg Reduction Using Panel Approach

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Big Data Analytics (BDA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7678))

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Abstract

Reduction to Hessenberg form is a major performance bottleneck in the computation of the eigenvalues of a nonsymmetric matrix; which takes O(N 3) flops. All the known blocked and unblocked direct Hessenberg reduction algorithms have an I/O complexity of O(N 3/B). To improve the performance by incorporating matrix-matrix operations in the computation, usually the Hessenberg reduction is computed in two steps: the first reducing the matrix to a banded Hessenberg form, and the second further reducing it to Hessenberg form. We propose and analyse the first step of the reduction, i.e., reduction of a nonsymmetric matrix to banded Hessenberg form of bandwidth t for varying values of N and M (the size of the internal memory), on external memory model introduced by Aggarwal and Vitter for the I/O complexity and show that the reduction can be performed in \(O(N^3/\min\{t,\sqrt{M}\}B)\) I/Os.

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Author information

Authors and Affiliations

  1. Computer Science & Engineering Discipline, PDPM Indian Institute of Information Technology, Design and Manufacturing Jabalpur, Jabalpur, 482005, MP, India

    Sraban Kumar Mohanty

  2. Computer Science & Engineering Department, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India

    Gopalan Sajith

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  1. Sraban Kumar Mohanty
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  2. Gopalan Sajith
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Editors and Affiliations

  1. International Institute of Information Technology Bangalore (IIIIT Bangalore), 26/C, Electronics City, Hosur Road, 560100, Bangalore, India

    Srinath Srinivasa

  2. Faculty of Mathematical Sciences, Department of Computer Science, University of Delhi, Delhi, India

    Vasudha Bhatnagar

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Mohanty, S.K., Sajith, G. (2012). I/O Efficient Algorithms for Block Hessenberg Reduction Using Panel Approach. In: Srinivasa, S., Bhatnagar, V. (eds) Big Data Analytics. BDA 2012. Lecture Notes in Computer Science, vol 7678. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35542-4_12

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  • DOI: https://doi.org/10.1007/978-3-642-35542-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35541-7

  • Online ISBN: 978-3-642-35542-4

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