GENERALISASI METODE DEKOMPOSISI COLESKY UNTUK MENYELESAIKAN SISTEM PERSAMAAN MATRIKS INTERVAL
Kata Kunci:
Generalisasi Dekomposisi Cholesky, Matriks Interval, Sistem Persamaan Matriks IntervalAbstrak
Suatu matriks interval adalah suatu matriks yang elemen-elemennya adalah suatu interval tertutup. Suatu matriks A simetris real dengan semua nilai eigennya lebih dari nol dapat diubah dalam bentuk dekomposisi Cholesky A=LLT , di mana adalah matriks segitiga bawah dan LT adalah transpos dari matriks . Tujuan dari penulisan artikel ini yaitu untuk mengetahui bagaimanakah generalisasi metode dekomposisi Cholesky untuk menyelesaikan sistem persamaan matriks interval
Referensi
Alefeld, G. and Herzberger, J. 1983. Introduction to Interval Computations, Academic Press, New York (1983).
Alefeld, G. and Gunter Mayer. 2000. Interval analysis: theory and applications. Journal of Computational and Applied Mathematics. 121 (2000) 421-464.
Ganesan, K., P. Veeramani, On arithmetic operations of interval numbers, International Journal of Uncertainty, Fuzziness and Knowledge – Based Systems, 13, No. 6 (2005), 619-631, doi: 10.1142/S0218488505003710.
Goldsztejn, Alexandre and Chabert, Gilles. 2007. A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems. Springer-Verlag Berlin Heidelberg. 312-319.
Hansen, E.R. and Smith, R.R. Interval arithmetic in matrix computations, Part 2, SIAM. journal of Numerical Analysis, 4 (1967), 1-9.
Kandasamy, Vasantha and Smarandance Florentin. 2011. Algebraic Structures Using Super Interval Matrices.
Kandasamy, Vasantha and Smarandance Florentin. 2010. Interval Linear Algebra. Glendale: Kappa & Omega.
Kandasamy, Vasantha and Smarandance Florentin. 2006. Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications. Phoenix: Hexis.
Kaucher E., Interval analysis in the extended interval space IR, Computing, Suppl., 2 (1980), 33-49, doi: 10.1007/978-3-7091-8577-3.
Moore, Ramon E., Kearfott, Ralph Baker and Cloud, Michael J. 2009. Introduction to interval analysis. Philadelphia: Society for Industrial and Applied Mathematics.
Nirmala, T., Datta, D., Kushwaha, H.S., Ganesan, K. 2013. The Determinant of An Interval Matrix Using Gaussian Elimination Method. International Journal of Pure and Applied Mathematics. Volume 88 No. 1 2013, 15-34.
Nirmala, T., Datta, D., Kushwaha, H.S., Ganesan, K, Inverse interval matrix: A new approach, Applied Mathematical Sciences, 5, No. 13 (2011), 607-624.
Neumaier, A. 1990. Interval Methods for Systems of Equations. Cambridge: Cambridge University Press.
Press, William H., Teukolsky Saul A., Vetterling William T., and Flannery Brian P. 1992. Numerical Recipes in C, The Art of Scientific Computing Second Edition. United States of Ammerica : Cambridge University Press.
Shary, Sergey P. 2001. Interval Gauss-Seidel Method for Generalized Solution Sets to Interval Linear Systems. Netherlands : Kluwer Academic Publishers 7: 141–155.
Wijna, Wihikan Mawi. 2009. Dekomposisi Matriks. Yogyakarta: wijna.web.ugm.ac.id.
Alefeld, G. and Gunter Mayer. 2000. Interval analysis: theory and applications. Journal of Computational and Applied Mathematics. 121 (2000) 421-464.
Ganesan, K., P. Veeramani, On arithmetic operations of interval numbers, International Journal of Uncertainty, Fuzziness and Knowledge – Based Systems, 13, No. 6 (2005), 619-631, doi: 10.1142/S0218488505003710.
Goldsztejn, Alexandre and Chabert, Gilles. 2007. A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems. Springer-Verlag Berlin Heidelberg. 312-319.
Hansen, E.R. and Smith, R.R. Interval arithmetic in matrix computations, Part 2, SIAM. journal of Numerical Analysis, 4 (1967), 1-9.
Kandasamy, Vasantha and Smarandance Florentin. 2011. Algebraic Structures Using Super Interval Matrices.
Kandasamy, Vasantha and Smarandance Florentin. 2010. Interval Linear Algebra. Glendale: Kappa & Omega.
Kandasamy, Vasantha and Smarandance Florentin. 2006. Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications. Phoenix: Hexis.
Kaucher E., Interval analysis in the extended interval space IR, Computing, Suppl., 2 (1980), 33-49, doi: 10.1007/978-3-7091-8577-3.
Moore, Ramon E., Kearfott, Ralph Baker and Cloud, Michael J. 2009. Introduction to interval analysis. Philadelphia: Society for Industrial and Applied Mathematics.
Nirmala, T., Datta, D., Kushwaha, H.S., Ganesan, K. 2013. The Determinant of An Interval Matrix Using Gaussian Elimination Method. International Journal of Pure and Applied Mathematics. Volume 88 No. 1 2013, 15-34.
Nirmala, T., Datta, D., Kushwaha, H.S., Ganesan, K, Inverse interval matrix: A new approach, Applied Mathematical Sciences, 5, No. 13 (2011), 607-624.
Neumaier, A. 1990. Interval Methods for Systems of Equations. Cambridge: Cambridge University Press.
Press, William H., Teukolsky Saul A., Vetterling William T., and Flannery Brian P. 1992. Numerical Recipes in C, The Art of Scientific Computing Second Edition. United States of Ammerica : Cambridge University Press.
Shary, Sergey P. 2001. Interval Gauss-Seidel Method for Generalized Solution Sets to Interval Linear Systems. Netherlands : Kluwer Academic Publishers 7: 141–155.
Wijna, Wihikan Mawi. 2009. Dekomposisi Matriks. Yogyakarta: wijna.web.ugm.ac.id.
Unduhan
Diterbitkan
2014-08-14
Cara Mengutip
Na’imah, S., Warli, & Fadiana, M. (2014). GENERALISASI METODE DEKOMPOSISI COLESKY UNTUK MENYELESAIKAN SISTEM PERSAMAAN MATRIKS INTERVAL. Prosiding Seminar Nasional Matematika Dan Pendidikan Matematika, 5(1), 427–436. Diambil dari http://prosiding.unirow.ac.id/index.php/snmpm/article/view/60
Terbitan
Bagian
Articles
