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
@article{DeSDeM:96-24,
author = {De Schutter, Bart and De Moor, Bart},
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}
}