A Note On Advanced Normalization Algorithms And Their Applications.

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Bibliographic Details
Title:	A Note On Advanced Normalization Algorithms And Their Applications.
Authors:	B., Amutha¹ amuthab51@gmail.com, R., Perumal² perumalr@srmist.edu.in, J., Jackson³ jj3375@srmist.edu.in, S., Senthil⁴ senthilsports@yahoo.co.in
Source:	IAENG International Journal of Computer Science. Jul2025, Vol. 52 Issue 7, p2445-2452. 8p.
Subjects:	Addition (Mathematics), Circulant matrices, Linear systems, Degrees of freedom, Arithmetic
Abstract:	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 ≠ 0 and T ๏ x = 0. We have given some important results on the principal solution of the max linear system. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	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 ≠ 0 and T ๏ x = 0. We have given some important results on the principal solution of the max linear system. [ABSTRACT FROM AUTHOR]
ISSN:	1819656X