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Vol 15 No 4 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Articles

MASALAH EIGEN DAN EIGENMODE MATRIKS ATAS ALJABAR MIN-PLUS

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  • Eka Widia Rahayu,
  • Siswanto Siswanto,
  • Santoso Budi Wiyono
Eka Widia Rahayu
UNS
Siswanto Siswanto
Universitas Sebelas Maret
Santoso Budi Wiyono
Universitas Sebelas Maret
DOI: https://doi.org/10.30598/barekengvol15iss4pp659-666
Published December 1, 2021
Keywords
  • Aljabar min-plus,
  • masalah eigen,
  • eigenmode
How to Cite
[1]
E. Rahayu, S. Siswanto, and S. B. Wiyono, “MASALAH EIGEN DAN EIGENMODE MATRIKS ATAS ALJABAR MIN-PLUS”, BAREKENG: J. Math. & App., vol. 15, no. 4, pp. 659-666, Dec. 2021.
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Abstract

Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph. The communication graph can be strongly connected graph and a not strongly connected graph. The representation matrix of a strongly connected graph is called an irreducible matrix, while the representation matrix of a graph that is not strongly connected is called a reduced matrix. The purpose of this research is set the steps to determine the eigenvalues and eigenvectors of the irreducible matrix over min-plus algebra and also eigenmode of the regular reduced matrix over min-plus algebra. Min-plus algebra has an ispmorphic structure with max-plus algebra. Therefore, eigen problems and eigenmode matrices over min-plus algebra can be determined based on the theory of eigenvalues, eigenvectors and eigenmode matrices over max-plus algebra. The results of this research obtained steps to determine the eigenvalues and eigenvectors of the irreducible matrix over min-plus algebra and eigenmode algorithm of the regular reduced matrix over min-plus algebra

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References

  1. DAFTAR PUSTAKA
  2. Baccelli, F., et al, Synchronization and Linearity, New York: John Wiley and Sons, 2001.
  3. Konigsberg, Z.R., “A Generalized Eigenmode Algorithm for Reducible Regular Matrices over the Max-Plus Algebra”, International Matemathical Forum, 4.24. 1157-1171, 2009.
  4. Mursyidah, H. Subiono, “Eigenvalue, Eigenvector, Eigenmode of Reducible Matrix and Its Application”, Journal of AIP Conference Proccedings 020044: 1-14, 2017.
  5. Wibowo, A., Wijayanti, K. & Veronica, R.B.,” Penerapan Aljabar Max-Plus pada Pengaturan Sistem Antrian Traffic light”, Unnes Journal of Mathematics 7(2): 192-205, 2018.
  6. Farlow, K.G., Maxplus Algebra, Master’s thesis, Virginia Polytechnic, Institut and State University, Virginia, 2009.
  7. Tam, K.P., Optimizing and Approximating Eigenvectors in Max Algebra, A thesis Submitted to the University of Birmingham for The Degree of Doctor of Philosophy (PHD), 2010.
  8. Novrida, R., .Nilai Eigen dan Vektor Eigen dalam Aljabar Max-Plus, Tesis Program Pasca Sarjana UI, Depok :UI, 2012.
  9. Musthofa & Bintari, N., Sifat–Sifat Nilai Eigen dan Vektor Eigen atas Aljabar Max Plus, Jurnal Sains Dasar 2(1): 25-31, 2013.
  10. Tunisa, K., Wijayanti, K. dan Veronica, R.B., Nilai Eigen dan Vektor Eigen Matriks atas Aljabar Max-Plus. Unnes Journal of Mathematics 6(2): 189-197, 2017.
  11. Zuliyanto, A., Algoritma Eigenmode Tergeneralisasi untuk Matriks Terreduksi Reguler di dalam Aljabar Maks-Plus, Tugas Akhir untuk memperoleh Gelar Sarjana Matematika pada Jurusan Matematika pada Universitas Sebelas Maret Surakarta, 2012.
  12. Fitria, I., Eigenmode Matriks atas Aljabar Max-Plus, Tugas Akhir untuk memperoleh Gelar Sarjana Sains pada Jurusan Matematika pada Universitas Negeri Semarang, 2019.
  13. Nowak, A. W., The Tropical Eigen Value-Vector Problem from Algebraic, Graphical, and Computational Perspectives, A Thesis Submitted to The University of Bates Colleges for the Degree of Doctor of Philosophy (PHD),2014.
  14. Watanabe, S. & Watanabe, Y., Min-Plus Algebra and Network, Research Institute for Mathematical Sciences Kyoto University, 041-054, 2014.
  15. Nasichuddin, M., Aplikasi Aljabar Min-Plus dalam Menghitung Nilai Eigen dan Vektor Eigen pada Matriks n×n, Tugas Akhir untuk memperoleh Gelar Sarjana Matematika pada Jurusan Matematika pada Universitas Islam Negeri Maulana Malik Ibrahim Malang, 2018.
  16. Subiono, Aljabar Min-Max Plus dan Penerapannya, 3th ed., Institut Teknologi Sepuluh November, Surabaya, 2015.