Algorithms for computing signs of 2 x 2 determinants: Dynamics and average-case analysis

  • Brigitte Vallée
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1284)


An algorithm for computing signs of 2 x 2 determinants is analysed. Equivalently, this algorithm compares two rationals by using their continued fraction expansions. It is shown that the algorithm has similarities with the usual algorithm that operates with expansions in base b. The worst-case number of iterations is linear in the size of the entries. In contrast, the average number of iterations is found to be asymptotically constant and thus essentially independent of the size of data. The distribution of the number of iterations decays geometrically. The constants that intervene in the analysis are related to the spectral properties of transfer operators arising in dynamical systems theory.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Brigitte Vallée
    • 1
  1. 1.GREYC-URA 1526, Département d'InformatiqueUniversité de CaenCaen CedexFrance

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