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Ultima descărcare din IBN: 2022-04-21 22:22 |
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519.2+519.8 (3) |
Probability. Mathematical statistics (80) |
Operational research (OR): mathematical theories and methods (168) |
SM ISO690:2012 LAZARI, Alexandru, LOZOVANU, Dmitrii. New Algorithms for Finding the Limiting and Differential Matrices in Markov Chains. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, nr. 1(92), pp. 75-88. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | |||||||
Numărul 1(92) / 2020 / ISSN 1024-7696 /ISSNe 2587-4322 | |||||||
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CZU: 519.2+519.8 | |||||||
MSC 2010: 65C40, 60J22, 90C40, 65F05, 65F15, 15B51. | |||||||
Pag. 75-88 | |||||||
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New algorithms for determining the limiting and differential matrices in Markov chains, using fast matrix multiplication methods, new computation procedure of the characteristic polynomial and algorithms of resuming matrix polynomials, are proposed. We show that the complexity of finding the limiting matrix is O(n3) and the complexity of calculating differential matrices is O(n!+1), where n is the number of the states of the Markov chain and O(n!) is the complexity of the used matrix multiplication algorithm. The theoretical computational complexity estimation of the algorithm is governed by the fastest known matrix multiplication algorithm, for which ! < 2.372864. |
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Cuvinte-cheie Discrete Markov Process, The Matrix of Limiting States Probabilities, Differential Matrices, Matrix Multiplication Complexity |
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