The QR Decomposition and the Singular Value Decomposition in the Symmetrized Max-Plus Algebra Revisited
Citations
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Cites methods from "The QR Decomposition and the Singul..."
...The inverse of a matrix can be computed using many methods [23], such as Gauss-Jordan elimination, LU decomposition (also called LU factorization) [19], Singular Value Decomposition (SVD) [27], and QR decomposition [7]....
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Cites background or methods from "The QR Decomposition and the Singul..."
...The maxplus Singular Value Decomposition (SVD) of a max-plus matrix was introduced by De Schutter and De Moor in [2]....
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...Theorem 1.6 (De Schutter, De Moor [2]) Let G = (gij) ∈ Rn×nmax be a max-plus matrix and let B = (bij) ∈ Cn×n be a complex matrix....
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...6 (De Schutter, De Moor [2]) Let G = (gij) ∈ Rn×n max be a max-plus matrix and let B = (bij) ∈ Cn×n be a complex matrix....
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...De Schutter and De Moore also use the decomposition to introduce a definition of the rank of a max-plus matrix, which ∗School of Mathematics, The University of Manchester, Manchester, M13 9PL, UK (james.hook@manchester.ac.uk)....
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References
20,436 citations
"The QR Decomposition and the Singul..." refers background or methods in this paper
...The QRD and the SVD are used in many contemporary algorithms for the identification of conventional linear systems [44, 45, 50, 60, 61, 62, 63]....
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...These matrix decompositions are important tools in many linear algebra algorithms (see [31, 40, 41, 59] and the references cited therein), and in many contemporary algorithms for the identification of linear systems (see [44, 45, 50, 60, 61, 62, 63] and the references cited therein)....
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4,330 citations
"The QR Decomposition and the Singul..." refers methods in this paper
...There exist many different modeling and analysis frameworks for discrete-event systems such as Petri nets, finite state machines, queuing networks, automata, semi-Markov processes, max-plus algebra, formal languages, temporal logic, perturbation analysis, process algebra, and computer models [1, 5, 24, 37, 38, 39, 57, 64]....
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1,921 citations
646 citations
"The QR Decomposition and the Singul..." refers background or methods in this paper
...The QRD and the SVD are used in many contemporary algorithms for the identification of conventional linear systems [44, 45, 50, 60, 61, 62, 63]....
[...]
...These matrix decompositions are important tools in many linear algebra algorithms (see [31, 40, 41, 59] and the references cited therein), and in many contemporary algorithms for the identification of linear systems (see [44, 45, 50, 60, 61, 62, 63] and the references cited therein)....
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584 citations
"The QR Decomposition and the Singul..." refers methods in this paper
...There exist many different modeling and analysis frameworks for discrete-event systems such as Petri nets, finite state machines, queuing networks, automata, semi-Markov processes, max-plus algebra, formal languages, temporal logic, perturbation analysis, process algebra, and computer models [1, 5, 24, 37, 38, 39, 57, 64]....
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