METHODS AND SYSTEMS OF INFORMATION PROTECTION, INFORMATION SECURITY

About the construction of spatial-decomposition algorithm based on the ellipsoids adaptive algorithm geometric parallelization

I. I. Lapikov

the Fund of assistance to development of secure information technologies

Abstract: The article considers the concept of an adaptive algorithm for solving systems of linear inequalities with k- valued unknowns based on the ideas of the Hachiyans ellipsoids method. In-depth study of the ellipsoids adaptive algorithm application practical aspects and convergence allowed us to identify additional exit criteria, which significantly accelerate its work, particularly in the proof of inequalities systems incompatibility case. On the basis of the obtained results, a spatial-decomposition algorithm, which based on the spatial decomposition of linear inequalities with k- valued unknowns system solutions initial localization region and the ellipsoids adaptive algorithm geometric parallelization, is constructed.

Keywords: systems of linear inequalities systems, k-valued logic, ellipsoid method, geometric parallelization, the ellipsoids adaptive algorithm, spatial decomposition, SD-algorithm.

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