ABOUT THE CONSTRUCTION OF SPATIAL-DECOMPOSITION ALGORITHM BASED ON THE ELLIPSOIDS ADAPTIVE ALGORITHM GEOMETRIC PARALLELIZATION
( Pp. 140-145)

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Lapikov Igor I. Cand. Sci. (Eng.); аssociate professor at the Cybersecurity and Digital Technologies Institute of the Russian Technological
MIREA - Russian Technological University
Moscow, Russian Federation
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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.
How to Cite:
Lapikov I.I., (2018), ABOUT THE CONSTRUCTION OF SPATIAL-DECOMPOSITION ALGORITHM BASED ON THE ELLIPSOIDS ADAPTIVE ALGORITHM GEOMETRIC PARALLELIZATION. Computational Nanotechnology, 1 => 140-145.
Reference list:
Lapikov I.I., Nikonov V.G. Adaptivnyy algoritm resheniy sistem neravenstv s k-znachnymi neizvestnymi. // Trudy Voenno-kosmicheskoy akademii im. A.F. Mozhayskogo. Vyp. № 1. SPB.: VKA im. A.F. Mozhayskogo, 2016. S. 88-94
KHachiyan L.G. Polinomial nyy algoritm v lineynom programmirovanii // Dokl. AN SSSR. T. 244, № 5, 1978. S. 1093-1096.
Balakin G.V., Nikonov V.G. Metody svedeniya bulevykh uravneniy k sistemam porogovykh sootnosheniy // Obzor prikl. promyshlennoy matem. Ser. Diskret. matem. . T. 1, № 3, 1994. S. 389-401.
Nikonov N.V., Rybnikov K.K. Prikladnye zadachi, svodyashchiesya k analizu i resheniyu sistem lineynykh neravenstv. Metod razdelyayushchikh ploskostey // Vestnik MGUL Lesnoy vestnik , № 2 (22), 2002. S. 191-195.
Nikonov V.G., Nikonov N.V. Osobennosti porogovykh predstavleniy k-znachnykh funktsiy // Tr. po diskr. matem. T. 11, 2008. S. 60-85.
Lapikov I.I. Primenenie poliedral nogo metoda dlya vosstanovleniya lineynoy rekurrenty, realizovannoy lineynym registrom sdviga s trekhchlennym zakonom obratnoy svyazi, po ee starshey koordinatnoy posledovatel nosti // Trudy SPIIRAN, № 3 (58), 2018 (prinyata k pechati).
Lapikov I.I. O vozmozhnosti geometricheskogo rasparallelivaniya adaptivnogo algoritma resheniya sistem neravenstv s k-znachnymi neizvestnymi na baze metoda ellipsoidov KHachiyana // Sistemy upravleniya i informatsionnye tekhnologii. № 2, 2016. S. 14-19.
KHachiyan L.G. Polinomial nye algoritmy v lineynom programmirovanii // ZHurnal vychislitel noy matematiki i matematicheskoy fiziki. T. 20, 1980.
KHachiyan L.G. Slozhnost vypuklykh zadach veshchestvennogo i tselochislennogo polinomial nogo programmirovaniya: diss.. doktora fiz.-mat. nauk: 05.13.02. - Moskva, 1983. 252 c.
Keywords:
systems of linear inequalities, k-valued logic, method of ellipsoids, geometric parallelization], the adaptive algorithm of ellipsoids, spatial decomposition, PD-algorithm.


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