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Universal algorithms, mathematics of semirings and parallel computations

Universal algorithms, mathematics of semirings and parallel computations

Authors :
Litvinov, G. L.
Maslov, V. P.
Rodionov, A. Ya.
Sobolevski, A. N.
Litvinov, G. L.
Maslov, V. P.
Rodionov, A. Ya.
Sobolevski, A. N.
Publication Year :
2010

Abstract

This is 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.<br />Comment: 36 pages, 1 figure. To appear in Springer Lecture Notes in Computational Science and Engineering.

Details

Database :
OAIster
Publication Type :
Electronic Resource
Accession number :
edsoai.ocn691097943
Document Type :
Electronic Resource