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A Note On Advanced Normalization Algorithms And Their Applications.

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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]
Copyright of IAENG International Journal of Computer Science is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A Note On Advanced Normalization Algorithms And Their Applications.
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Computer+Science%22">IAENG International Journal of Computer Science</searchLink>. Jul2025, Vol. 52 Issue 7, p2445-2452. 8p.
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  Data: <searchLink fieldCode="DE" term="%22Addition+%28Mathematics%29%22">Addition (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Circulant+matrices%22">Circulant matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Degrees+of+freedom%22">Degrees of freedom</searchLink><br /><searchLink fieldCode="DE" term="%22Arithmetic%22">Arithmetic</searchLink>
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of IAENG International Journal of Computer Science is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 8
        StartPage: 2445
    Subjects:
      – SubjectFull: Addition (Mathematics)
        Type: general
      – SubjectFull: Circulant matrices
        Type: general
      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Degrees of freedom
        Type: general
      – SubjectFull: Arithmetic
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      – TitleFull: A Note On Advanced Normalization Algorithms And Their Applications.
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            NameFull: R., Perumal
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            – D: 01
              M: 07
              Text: Jul2025
              Type: published
              Y: 2025
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