CHARACTERIZATION OF THE SOLUTIONS OF INTERVAL SYSTEM OF LINEAR EQUATIONS OVER INTERVAL SUPERTROPICAL ALGEBRA
DOI:
https://doi.org/10.24269/silogisme.v8i1.6945Abstract Penelitian ini bertujuan untuk mediskusikan mengenai solusi dari sistem persamaan interval atas aljabar supertropical. Aljabar supertropical merupakan semiring komutatif dengan ghost. Sistem persamaan linear interval pada aljabar supertropical diberikan oleh persamaan matriks  dengan  adalah matriks interval  adalah vector interval, dan  merupakan vektor interval yang merupakan solusi dari system persamaan linear interval. Pada peneletian ini ditunjukkan syarat perlu dan syarat cukup dari solusi sistem persamaan linear interval serta ditunjukkan bahwa terdapat dua tipe solusi dari sistem persamaan linear interval atas aljabar supertropical
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Wang, L., Li, W., & Li, H. (2018). AE solutions to two-sided interval linear systems over max-plus algebra. Journal of Inequalities and Applications, 2018, 1–13. https://doi.org/10.1186/s13660-018-1869-6
Yuliati, D. (2016). Characterization of The Solution of Non Homogeneous System of Linear Equations Over Supertropical Algebra. 321–325.
Izhakian, Z. (2019). Commutative $\nu$-algebra and supertropical algebraic geometry. 1–83.
Izhakian, Z., & Rowen, L. (2010a). A guide to supertropical algebra. Trends in Mathematics, 49, 283–302. https://doi.org/10.1007/978-3-0346-0286-0_19
Izhakian, Z., & Rowen, L. (2010b). Supertropical algebra. Advances in Mathematics, 225(4), 2222–2286. https://doi.org/10.1016/j.aim.2010.04.007
Izhakian, Z., & Rowen, L. (2011a). Supertropical matrix algebra. Israel Journal of Mathematics, 182(1), 383–424.
https://doi.org/10.1007/s11856-011-0036-2
Izhakian, Z., & Rowen, L. (2011b). Supertropical matrix algebra III: Powers of matrices and their supertropical eigenvalues. Journal of Algebra, 341(1), 125–149. https://doi.org/10.1016/j.jalgebra.2011.06.002
Jones, D. (2021). Matrix roots in the max-plus algebra. Linear Algebra and Its Applications, 631, 10–34. https://doi.org/10.1016/j.laa.2021.08.008
Komenda, J., Lahaye, S., Boimond, J. L., & van den Boom, T. (2017). Max-Plus Algebra and Discrete Event Systems. IFAC-PapersOnLine, 50(1), 1784–1790. https://doi.org/10.1016/j.ifacol.2017.08.163
Kurniawan, A., Suparwanto, A. R. I., & Max-plus, A. (2020). sistem persamaan linear max-plus dan terapannya pada sistem jaringan kereta api ( max-plus linear equation system and its application on railway network system ). 02(01), 63–77.
Myšková, H. (2005). Interval systems of max-separable linear equations. Linear Algebra and Its Applications, 403(1–3), 263–272. https://doi.org/10.1016/j.laa.2005.02.011
Myšková, H. (2012). Interval max-plus systems of linear equations. Linear Algebra and Its Applications, 437(8), 1992–2000. https://doi.org/10.1016/j.laa.2012.04.051
Niv, A. (2015). On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra. In Linear Algebra and Its Applications (Vol. 471, pp. 264–290). https://doi.org/10.1016/j.laa.2014.12.038
Rudhito, M. A., Wahyuni, S., Suparwanto, A., & Susilo, F. (2012). Matriks atas Aljabar Max-Plus Interval. Jurnal Natur Indonesia, 13(2), 94. https://doi.org/10.31258/jnat.13.2.94-99
Wang, L., Li, W., & Li, H. (2018). AE solutions to two-sided interval linear systems over max-plus algebra. Journal of Inequalities and Applications, 2018, 1–13. https://doi.org/10.1186/s13660-018-1869-6
Yuliati, D. (2016). Characterization of The Solution of Non Homogeneous System of Linear Equations Over Supertropical Algebra. 321–325.
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2023-06-08
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