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.