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Real Root Isolation of Multi-Exponential Polynomials with Application

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WALCOM: Algorithms and Computation (WALCOM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5942))

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Abstract

Real root isolation problem is to compute a list of disjoint intervals, each containing a distinct real root and together containing all. Traditional methods and tools often attack the root isolation for ordinary polynomials. However many other complex systems in engineering are modeling with non-ordinary polynomials. In this paper, we extend the pseudo-derivative sequences and Budan–Fourier theorem for multi-exponential polynomials to estimate the bounds and counts of all real roots. Furthermore we present an efficient algorithm for isolating all real roots under given minimum root separation. As a proof of serviceability, the reachability of linear systems with real eigenvalues only is approximately computable by this algorithm.

Supported by NSFC (No. 90718041), Shanghai Leading Academic Discipline Project (No. B412) and PhD Program Scholarship Fund of ECNU 2009 (No. 2009056).

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Author information

Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing,  

    Ming Xu, Liangyu Chen, Zhenbing Zeng & Zhi-bin Li

  2. Computer Science and Technology Department, East China Normal University, Shanghai, 200062, China

    Ming Xu & Zhi-bin Li

Authors
  1. Ming Xu
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  2. Liangyu Chen
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  3. Zhenbing Zeng
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  4. Zhi-bin Li
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), 1000, Dhaka, Bangladesh

    Md. Saidur Rahman

  2. Graduate School of Engineering, Department of Information Engineering, Hiroshima University, Kagamiyama 1-4-1, 739-8527, Higashi-Hiroshima, Japan

    Satoshi Fujita

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© 2010 Springer-Verlag Berlin Heidelberg

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Xu, M., Chen, L., Zeng, Z., Li, Zb. (2010). Real Root Isolation of Multi-Exponential Polynomials with Application. In: Rahman, M.S., Fujita, S. (eds) WALCOM: Algorithms and Computation. WALCOM 2010. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11440-3_24

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  • DOI: https://doi.org/10.1007/978-3-642-11440-3_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11439-7

  • Online ISBN: 978-3-642-11440-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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