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Title: Complete solution of tropical vector inequalities using matrix sparsification (English)
Author: Krivulin, Nikolai
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 65
Issue: 6
Year: 2020
Pages: 755-775
Summary lang: English
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Category: math
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Summary: We examine the problem of finding all solutions of two-sided vector inequalities given in the tropical algebra setting, where the unknown vector multiplied by known matrices appears on both sides of the inequality. We offer a solution that uses sparse matrices to simplify the problem and to construct a family of solution sets, each defined by a sparse matrix obtained from one of the given matrices by setting some of its entries to zero. All solutions are then combined to present the result in a parametric form in terms of a matrix whose columns form a complete system of generators for the solution. We describe the computational technique proposed to solve the problem, remark on its computational complexity and illustrate this technique with numerical examples. (English)
Keyword: tropical semifield
Keyword: tropical two-sided inequality
Keyword: matrix sparsification
Keyword: complete solution
Keyword: backtracking
MSC: 15A39
MSC: 15A80
MSC: 65F50
idZBL: Zbl 07285955
idMR: MR4191367
DOI: 10.21136/AM.2020.0376-19
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Date available: 2020-11-18T09:37:56Z
Last updated: 2021-04-08
Stable URL: http://hdl.handle.net/10338.dmlcz/148395
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