Solving Linear Systems over Idempotent Semifields through $LU$-factorization
Commutative Algebra
2019-06-24 v2
Abstract
In this paper, we introduce and analyze a new -factorization technique for square matrices over idempotent semifields. In particular, more emphasis is put on "max-plus" algebra here, but the work is extended to other idempotent semifields as well. We first determine the conditions under which a square matrix has factors. Next, using this technique, we propose a method for solving square linear systems of equations whose system matrices are -factorizable. We also give conditions for an -factorizable system to have solutions. This work is an extension of similar techniques over fields. Maple procedures for this -factorization are also included.
Keywords
Cite
@article{arxiv.1904.13256,
title = {Solving Linear Systems over Idempotent Semifields through $LU$-factorization},
author = {Sedighe Jamshidvand and Shaban Ghalandarzadeh and Amirhossein Amiraslani and Fateme Olia},
journal= {arXiv preprint arXiv:1904.13256},
year = {2019}
}