The QR decomposition and the singular value decomposition in the symmetrized max-plus algebra


Reference:
B. De Schutter and B. De Moor, "The QR decomposition and the singular value decomposition in the symmetrized max-plus algebra," SIAM Journal on Matrix Analysis and Applications, vol. 19, no. 2, pp. 378-406, Apr. 1998.

Abstract:
In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algorithms from linear algebra to prove the existence of max-algebraic analogues of the QR decomposition, the singular value decomposition, the Hessenberg decomposition, the LU decomposition and so on.


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Bibtex entry:

@article{DeSDeM:96-24,
        author={B. {De Schutter} and B. {De Moor}},
        title={The {QR} decomposition and the singular value decomposition in the symmetrized max-plus algebra},
        journal={SIAM Journal on Matrix Analysis and Applications},
        volume={19},
        number={2},
        pages={378--406},
        month=apr,
        year={1998},
        doi={10.1137/S0895479896304782}
        }



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