APLIKASI ALGORITMA LEVERRIER FADDEEV DALAM MENGHITUNG INVERS MATRIKS CENTROSYMMETRIC
DOI:
https://doi.org/10.25077/jmua.13.4.324-339.2024Keywords:
Algoritma Leverrier Faddeev, invers, matriks centrosymmetric, nilai eigenAbstract
Matriks centrosymmetric adalah matriks bentuk khusus dari matriks simetris, yang mana matriks ini memiliki struktur simetri pada pusat matriksnya. Di antara beberapa masalah terkait matriks centrosymmetric adalah masalah penentuan invers dan nilai eigennya. Pada penelitian ini dikaji masalah penentuan invers dan nilai eigen dari matriks centrosymmetric dengan bentuk khusus ordo n × n, n ≥ 3 dengan menggunakan algoritma Leverrier Faddeev. Penelitian ini diawali dengan menentukan Yi dan qi dari setiap matriks centrosymmetric berukuran n × n, 3 ≥ n ≥ 8. Selanjutnya dengan memperhatikan pola invers dan nilai eigennya diperoleh bentuk umum invers dan nilai eigen dari matriks centrosymmetric dengan bentuk khusus ordo n × n, n ≥ 3 dalam dua kasus, yaitu untuk n = 2m + 1 dan n = 2m.References
Anton, H., dan Rorres, C., 2013, Aljabar Linear Elementer Edisi Versi Aplikasi,
Edisi Ke-11, Erlangga, Jakarta
Bronson, R. dan Gabriel B., 2007, Linear Algebra An Introduction Second
Edition, Elsevier’s Science and Technology Rights Departemen in Oxford, UK
Caltenco, J., 2007, Characteristic polynomial of A and faddeev’s method for
A−1
, Educatia Matematica, 3: 107-112
Datta, L and Morgera, S., 1989, On the reducibility of centrosymmetric
matrices-applications in engineering problems, Circuits System Signal Process,
Fatoorehchi, H., Hossein, A., 2014, On computation of real eigenvalues of
matrices via the adomian decomposition, Egyptian Mathematical Society, 22
(1 ): 6-10
Gentle, J., 2017, Matrix Algebra Theory, Computations and Applications in
Statistics Second Edition, Springer International Publishing AG, Switzerland
Gower, J., 2006, An application of the modified leverrier faddeev algorithm
to the spectral decomposition of symmetric block-circulant matrices,
Computational Statistics and Data analysis, 50: 89-106
Hendricks, E., Jannerup, O., S⊘rensen, P., 2008, Linear Systems Control,
Springer, Berlin
James E., 2007, Matrix Algebra, Springer, New York
Katsuhiko O., 1997, Modern Control Engineering, 3rd, Prentice Hall, Inc. USA
Koohestani, K., 2017, On the analytical form-finding of tensegrities, Composite
Structure, 166: 114-119
Hanna, M., Mansoori, S., 2003, A centrosymmetric matrix based technique for
the interpolation of hermitian signal, Numerical Linear Algebra with Appl, 10:
-720
Rosen, K., 2007, Discrete Mathematics and Its Application, Edisi ke-7,
McGraw-Hill, Singapore
Tamasouw, B., 2016, Karekteristik matriks centrosymmetric, Barekeng, 10:
-76
Teschl, G., 2014, Mathematical Methods in Quantum Mechanics: With
Application to Schro¨dinger Operators, American Mathematical Society
Tian, Z., Chuanqing G., 2007, The iterative methods for centrosymmetric
matrices, Applied Mathematics and Computation, 187: 902-911
Boyce, W., DiPrima, R., 2012, Elementary Differential Equations and
Boundary Value Problems, Edisi ke-10, New York
Downloads
Published
Issue
Section
License
All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.
Copyright Holder
The copyright of all articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND). This applies to all published versions, including the HTML and PDF formats of the articles.
Author Rights
While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:
- Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
- Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.
Creative Commons License (CC BY-SA)
Under the terms of the CC BY-SA license, users are free to:
- Share: Copy and redistribute the material in any medium or format.
- Adapt: Remix, transform, and build upon the material for any purpose, even commercially.
However, the following conditions apply:
- Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
- ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.
For more information about the CC BY-SA license, please visit the Creative Commons website.
Third-Party Content
If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.
Copyright and Licensing Information Display
The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.
No "All Rights Reserved"
As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.
Â
