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Solvability classes for core problems in matrix total least squares minimization

Iveta Hnětynková, Martin Plešinger, Jana Žáková (2019)

Applications of Mathematics

Linear matrix approximation problems $A X \approx B$ are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if $B$ is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of $B$ is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková,...

Solvability of infinite systems of linear equations

Alexander Abian (1976)

Archivum Mathematicum

Solving a family of permutation problems on 0-1 matrices

Gilbert Laporte (1987)

RAIRO - Operations Research - Recherche Opérationnelle

Solving Confluent Vandermonde Systems of Hermite Type.

G. Galimberti, V. Pereyra (1971/1972)

Numerische Mathematik

Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension.

Navarro, E., Jódar, L., Company, R. (1994)

International Journal of Mathematics and Mathematical Sciences

Solving linear systems with a Levinson-like solver.

Vandebril, Raf, Mastronardi, Nicola, Van Barel, Marc (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Solving systems of two–sided (max, min)–linear equations

Martin Gavalec, Karel Zimmermann (2010)

Kybernetika

A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.

Solving the sensor cover energy problem via integer linear programming

Pingke Li (2021)

Kybernetika

This paper demonstrates that the sensor cover energy problem in wireless communication can be transformed into a linear programming problem with max-plus linear inequality constraints. Consequently, by a well-developed preprocessing procedure, it can be further reformulated as a 0-1 integer linear programming problem and hence tackled by the routine techniques developed in linear and integer optimization. The performance of this two-stage solution approach is evaluated on a set of randomly generated...

This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties.