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Solving Linear Systems over Idempotent Semifields through\n LU-factorization

2019/04/30 by Sedighe Jamshidvand, Shaban Ghalandarzadeh, Jamshidvand, Sedighe +5
Computer Science · Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1904.13256

openalex publication_date 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce and analyze a new LU-factorization technique\nfor square matrices over idempotent semifields. In particular, more emphasis is\nput on "max-plus" algebra here, but the work is extended to other idempotent\nsemifields as well. We first determine the conditions under which a square\nmatrix has LU factors. Next, using this technique, we propose a method for\nsolving square linear systems of equations whose system matrices are\nLU-factorizable. We also give conditions for an LU-factorizable system to\nhave solutions. This work is an extension of similar techniques over fields.\nMaple procedures for this LU-factorization are also included.\n

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