On the rank-one approximation of positive matrices using tropical optimization methods

DOI10.1134/S1063454119020080zbMath1439.90053OpenAlexW2955621772MaRDI QIDQ2289366

Nikolai Krivulin, Elena Yu. Romanova

Publication date: 28 January 2020

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1063454119020080

zbMATH Keywords

max-algebratropical mathematicstropical optimizationlog-Chebyshev distance functionrank-one matrix approximation

Mathematics Subject Classification ID

Tropical optimization (e.g., max-plus optimization) (90C24)

Uses Software

• PROXIMUS

Cites Work

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• An extremal property of the eigenvalue of irreducible matrices in idempotent algebra and solution of the Rawls location problem
• Max-plus methods for nonlinear control and estimation.
• Rank-one approximation of positive matrices based on methods of tropical mathematics
• Low-rank matrix approximation in the infinity norm
• Extremal properties of tropical eigenvalues and solutions to tropical optimization problems
• Tropical optimization problems in time-constrained project scheduling
• Fast low rank approximations of matrices and tensors
• Numerical linear algebra in data mining
• Max-linear Systems: Theory and Algorithms
• Literature survey on low rank approximation of matrices
• Conditional Gradient Algorithmsfor Rank-One Matrix Approximations with a Sparsity Constraint

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