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Computation of Joint Spectral Radius for Network Model Associated with Rank-One Matrix Set

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Book cover Neural Information Processing (ICONIP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7665))

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Abstract

In the paper, we prove that any finite set of rank-one matrices has the finiteness property by making use of (invariant) extremal norm. An explicit formula for the computation of joint/generalized spectral radius of such type of matrix sets is derived. Several numerical examples from current literature are provided to illustrate our theoretical conclusion.

This work was supported by NSF 1021203 of the United States.

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Authors and Affiliations

  1. Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901-4408, USA

    Jun Liu & Mingqing Xiao

Authors
  1. Jun Liu
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  2. Mingqing Xiao
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Editor information

Editors and Affiliations

  1. Texas A&M University at Qatar, Education City, P.O. Box 23874, Doha, Qatar

    Tingwen Huang

  2. Department of Control Science and Engineering, Huazhong University of Science and Technology, 1037 Luoyu Road, 430074, Wuhan, Hubei, China

    Zhigang Zeng

  3. College of Computer Science, Chongqing University, 174 Shazhengjie Street, 400044, Chongqing, China

    Chuandong Li

  4. Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China

    Chi Sing Leung

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© 2012 Springer-Verlag Berlin Heidelberg

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Liu, J., Xiao, M. (2012). Computation of Joint Spectral Radius for Network Model Associated with Rank-One Matrix Set. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34487-9_44

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  • DOI: https://doi.org/10.1007/978-3-642-34487-9_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34486-2

  • Online ISBN: 978-3-642-34487-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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