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Real Root Isolation of Multi-Exponential Polynomials with Application

  • Ming Xu
  • Liangyu Chen
  • Zhenbing Zeng
  • Zhi-bin Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ming Xu
    • 1
    • 2
  • Liangyu Chen
    • 1
  • Zhenbing Zeng
    • 1
  • Zhi-bin Li
    • 1
    • 2
  1. 1.Shanghai Key Laboratory of Trustworthy Computing 
  2. 2.Computer Science and Technology DepartmentEast China Normal UniversityShanghaiChina

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