A Note On Advanced Normalization Algorithms And Their Applications

The max-plus semiring is a semiring where the addition operation is replaced with maximum operation and the multiplication operation is replaced with the usual addition. In this paper we suggest 'Advanced normalization method' and its algorithms to solve the max linear system and its appli...

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Vydáno v:IAENG international journal of computer science Ročník 52; číslo 7; s. 2445
Hlavní autoři: Amutha, B, Perumal, R, Jackson, J, Senthil, S
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hong Kong International Association of Engineers 01.07.2025
Témata:
Algorithms
Arithmetic
Linear systems
Mathematical analysis
Matrices (mathematics)
Matrix algebra
Multiplication
Rings (mathematics)
ISSN:1819-656X, 1819-9224
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Shrnutí:The max-plus semiring is a semiring where the addition operation is replaced with maximum operation and the multiplication operation is replaced with the usual addition. In this paper we suggest 'Advanced normalization method' and its algorithms to solve the max linear system and its applications are discussed. We use these algorithms to determine the existence, uniqueness and the principal solution of a max linear system. An important aspect of the advanced normalization method is finding the free variables and the leading variables of any solvable max linear system. We have also found the generalized principal solution of the max linear system with some special matrices such as row-wise arithmetic matrix, column-wise arithmetic matrix, ϕ- diagonal matrix, Jc×d(l) matrix, arithmetic circulant matrix. The generalized principal solution of the max linear system had been found in both cases, T x = u with u= Ͼ and T x = Ͼ. We have given some important results on the principal solution of the max linear system. Index Terms-Max linear systems, Principal solution, Degrees of freedom.
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ISSN:1819-656X
1819-9224