An algorithm to describe the solution set of any tropical linear system \(A \odot x = B \odot x\)

DOI10.1016/j.laa.2011.02.014zbMath1217.65076arXiv1007.5193OpenAlexW1771190050MaRDI QIDQ541953

Elisa Lorenzo García, M. J. de la Puente

Publication date: 8 June 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.5193

zbMATH Keywords

algorithmnumerical examplesiterative methodGaussian eliminationsystem of linear inequalitiestropical linear system

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Iterative numerical methods for linear systems (65F10) Direct numerical methods for linear systems and matrix inversion (65F05) Linear equations (linear algebraic aspects) (15A06)

Related Items

Weakly linear systems for matrices over the max-plus quantale, On the dimension of max-min convex sets, On the solution of a two-sided vector equation in tropical algebra, Computing the vertices of tropical polyhedra using directed hypergraphs, Weak dual residuations applied to tropical linear equations, Complete solution of tropical vector inequalities using matrix sparsification., Duality and interval analysis over idempotent semirings, On \(2 \times 2\) tropical commuting matrices

Cites Work

• Basic solutions of systems with two max-linear inequalities
• A decomposition formula of idempotent polyhedral cones based on idempotent superharmonic spaces
• On visualization scaling, subeigenvectors and Kleene stars in max algebra
• Minimax algebra and applications
• The equation \(A \otimes x = B \otimes y\) over \((\max,+)\)
• Tropical convexity
• Graphs, dioids and semirings. New models and algorithms.
• A strongly polynomial algorithm for solving two-sided linear systems in max-algebra
• Tropical and Idempotent Mathematics
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