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Universal Algorithms, Mathematics of Semirings and Parallel Computations

  • Grigory L. Litvinov
  • Victor P. Maslov
  • Anatoly Ya. Rodionov
  • Andrei N. Sobolevski
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 75)

Abstract

This isaut]Grigory L. Litvinovaut]Victor P. Maslovaut]Anatoly Ya. Rodionovaut]Andrei N. Sobolevskii a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are examined. A very brief introduction to mathematics of semirings (including idempotent and tropical mathematics) is presented. Concrete applications to optimization problems, idempotent linear algebra and interval analysis are indicated. It is known that some nonlinear problems (and especially optimization problems) become linear over appropriate semirings with idempotent addition (the so-called idempotent superposition principle). This linearity over semirings is convenient for parallel computations.

Keywords

Systolic Array Bellman Equation Correspondence Principle Closure Operation Universal Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

This work is partially supported by the RFBR grant 08-01-00601. The authors are grateful to A. G. Kushner for his kind help.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Grigory L. Litvinov
    • 1
    • 2
  • Victor P. Maslov
    • 3
  • Anatoly Ya. Rodionov
    • 2
  • Andrei N. Sobolevski
    • 1
    • 4
  1. 1.The J. V. Poncelet Laboratory (UMI 2615 CNRS)Independent University of MoscowMoscowRussia
  2. 2.D. V. Skobeltsyn Research Institute for Nuclear PhysicsMoscow State UniversityMoscowRussia
  3. 3.Faculty of PhysicsMoscow State UniversityMoscowRussia
  4. 4.A. A. Kharkevich Institute for Information Transmission ProblemsMoscowRussia

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