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.

Publisher page

Downloads

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}
   }


Go to the publications overview page.

This page is maintained by Bart De Schutter. Last update: March 16, 2026.