ALGORITMA UNTUK MENENTUKAN KEKOPOSITIFAN MATRIKS SIMETRIS BERUKURAN ð’ = ðŸ‘, ðŸ’, ðŸ“
Keywords:
Algoritma, matriks kopositif, matriks simetris.
Abstract
Matriks kopositif merupakan matriks simetris yang memenuhi sifat tertentu. Matriks ini dapat digunakan dalam menyelesaikan masalah pemrograman kuadratik, masalah kombinatorik dan persamaan diferensial. Dalam penelitian ini, akan dibentuk beberapa algoritma untuk memeriksa kekopositifan suatu matriks simetris yang berukuran n = 3, n = 4 dan n = 5.
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References
[1] L. D. Baumert, “Extreme Copositive Quadratic Forms,†Pacific J. Math., vol. 19, pp. 197-204, 1966.
[2] R. W. Farebrother, “Necessary and Sufficient Conditions for a Quadratic Form to be Positive whenever a Set of Linear Constraints is Satisfied,†Linear Algebra Appl., vol. 16, pp. 39-42, 1977.
[3] J. W. Gaddum, “Linear Inequalities and Quadratic Forms,†Pasific J. Math., vol. 8, pp. 411-414, 1958.
[4] D. H. Jacobson, Extentions of Linear Quadratic Control, Optimization, and Matrix Theory, New York: Academic, 1977.
[5] T. S. Motzkin, “Copositive Quadratic Forms,†National Bureau of Standards Report, pp. 11-22, 1952.
[6] L. E. Anderson, G. Chang dan T. Elfying, “Criteria for Copositive Matrices using Simplices and Barycentric Coordinates,†Linear Algebra Appl., vol. 220, pp. 9-30, 1995.
[7] K. P. Hadeler, “On Copositive Matrices,†Linear Algebra Appl., vol. 49, pp. 78-89, 1983.
[2] R. W. Farebrother, “Necessary and Sufficient Conditions for a Quadratic Form to be Positive whenever a Set of Linear Constraints is Satisfied,†Linear Algebra Appl., vol. 16, pp. 39-42, 1977.
[3] J. W. Gaddum, “Linear Inequalities and Quadratic Forms,†Pasific J. Math., vol. 8, pp. 411-414, 1958.
[4] D. H. Jacobson, Extentions of Linear Quadratic Control, Optimization, and Matrix Theory, New York: Academic, 1977.
[5] T. S. Motzkin, “Copositive Quadratic Forms,†National Bureau of Standards Report, pp. 11-22, 1952.
[6] L. E. Anderson, G. Chang dan T. Elfying, “Criteria for Copositive Matrices using Simplices and Barycentric Coordinates,†Linear Algebra Appl., vol. 220, pp. 9-30, 1995.
[7] K. P. Hadeler, “On Copositive Matrices,†Linear Algebra Appl., vol. 49, pp. 78-89, 1983.
Published
2015-12-01
How to Cite
[1]
B. Tomasouw, “ALGORITMA UNTUK MENENTUKAN KEKOPOSITIFAN MATRIKS SIMETRIS BERUKURAN ð’ = ðŸ‘, ðŸ’, 📔, BAREKENG: J. Math. & App., vol. 9, no. 2, pp. 89-96, Dec. 2015.
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