The Singular Value Decomposition in the Extended Max Algebra ∗
نویسندگان
چکیده
First we establish a connection between the field of the real numbers and the extended max algebra, based on asymptotic equivalences. Next we propose a further extension of the extended max algebra that will correspond to the field of the complex numbers. Finally we use the analogy between the field of the real numbers and the extended max algebra to define the singular value decomposition of a matrix in the extended max algebra and to prove its existence.
منابع مشابه
The Singular Value Decomposition and the QR Decomposition in the Extended Max Algebra
In this paper we present an alternative proof for the existence theorem of the singular value decomposition in the extended max algebra and we propose some possible extensions of the max-algebraic singular value decomposition. We also prove the existence of a kind of QR decomposition in the extended max algebra.
متن کاملThe singular value decomposition in the extended max algebra is an extended linear complementarity problem ∗
We show that the problem of finding a singular value decomposition of a matrix in the extended max algebra can be reformulated as an Extended Linear Complementarity Problem. This allows us to compute all the max-algebraic singular value decompositions of a matrix. This technique can also be used to calculate many other max-algebraic matrix decompositions.
متن کاملThe QR Decomposition and the Singular Value Decomposition in the Symmetrized Max-Plus Algebra Revisited
This paper is an updated and extended version of the paper “The QR decomposition and the singular value decomposition in the symmetrized max-plus algebra” (by B. De Schutter and B. De Moor, SIAM Journal on Matrix Analysis and Applications, vol. 19, no. 2, pp. 378–406, April 1998). The max-plus algebra, which has maximization and addition as its basic operations, can be used to describe and anal...
متن کاملThe QR decomposition and the singular value decomposition in thesymmetrized max - plus algebra 1
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 algori...
متن کاملThe QR decomposition and the singular value decomposition in the symmetrized max-plus algebra∗
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 algori...
متن کامل