GENERALISASI METODE DEKOMPOSISI LU ( DOOLITTLE DAN CROUT ) DAN LDU UNTUK MENYELESAIKAN SISTEM PERSAMAAN MATRIKS INTERVAL
Kata Kunci:
Generalisasi Dekomposisi LU dan LDU, Matriks Interval, Sistem Persamaan Matriks Interval.Abstrak
Suatu matriks interval adalah suatu matriks yang elemennya adalah suatu interval tertutup. Sedangkan suatu sistem persamaan matriks interval didefinisikan sebagai Ax=b di mana A,b,x terdiri dari matriks interval. Pada penelitian ini dibahas bagaimanakah generalisasi metode dekomposisi LU (Doolittle dan Crout) dan dekomposisi LDU untuk menyelesaikan sistem persamaan matriks interval.
Referensi
Alefeld, G. and Herzberger, J. 1983. Introduction to Interval Computations. New York : Academic Press.
Alefeld, G. and Gunter Mayer. 2000. Interval analysis: theory and applications. Journal of Computational and Applied Mathematics. 121 (2000) 421-464.
Chen, Guanrong and Pham, Trung T. 2001. Introduction to Fuzzy Sets, Fuzzy Logic, And Fuzzy Control Systems. United States of America: CRC Press LLC.
Goldsztejn, Alexandre and Chabert, Gilles. 2007. A Generalized Interval LU De- composition for the Solution of Interval Linear Systems. Germain: Springer-Verlag Berlin Heidelberg. 312-319.
Ganesan, K. and Veeramani, P. On Arithmetic Operations of Interval Numbers, In- ternational Journal of Uncertainty, Fuzziness and Knowledge Based Systems, 13 (6) (2005), 619 - 631.
Ganesan, K. On Some Properties of Interval Matrices, International Journal of Com- putational and Mathematical Sciences, 1 (2) (2007), 92-99.
Golub, Gane H., and Loan Charles F. Van. 1996. Matrix Computation Third Edition. United States of America: The Johns Hopkins University Press.
Hansen, E.R. and Smith, R.R. Interval arithmetic in matrix computations, Part 2, SIAM. journal of Numerical Analysis, 4 (1967), 1-9.
Hargreaves, Gareth I. 2002. Interval Analysis in Matlab. England: University of Manchester.
Harville, David A. 1997. Matrix Algebra From a Statistician's Perspective. New York : Springer-Verlag, Inc.
Kandasamy, Vasantha and Smarandance, Florentin. 2011. Algebraic Structures Us- ing Super Interval Matrices.
Kandasamy, Vasantha and Smarandance, Florentin. 2006. Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications. Phoenix: Hexis.
Kandasamy, Vasantha and Smarandance, Florentin. 2010. Interval Linear Algebra. Glendale: Kappa & Omega.
Kaucher, E. Interval Analysis in the Extended Interval Space . Computing, Suppl. 2 (1980), 33 - 49.
Lay, David C. 2006. Linear Algebra and Its Applications Third Edition Update. United States of America: Pearson Education, Inc.
Meyer, Carl D. 2000. Matrix Analysis and Applied Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics.
Moore, Ramon E., Kearfott, Ralph Baker and Cloud, Michael J. 2009. Introduction to interval analysis. Philadelphia: Society for Industrial and Applied Mathematics.
Neumaier, A. 1990. Interval Methods for Systems of Equations. United States of America: Cambridge University Press.
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.
Alefeld, G. and Gunter Mayer. 2000. Interval analysis: theory and applications. Journal of Computational and Applied Mathematics. 121 (2000) 421-464.
Chen, Guanrong and Pham, Trung T. 2001. Introduction to Fuzzy Sets, Fuzzy Logic, And Fuzzy Control Systems. United States of America: CRC Press LLC.
Goldsztejn, Alexandre and Chabert, Gilles. 2007. A Generalized Interval LU De- composition for the Solution of Interval Linear Systems. Germain: Springer-Verlag Berlin Heidelberg. 312-319.
Ganesan, K. and Veeramani, P. On Arithmetic Operations of Interval Numbers, In- ternational Journal of Uncertainty, Fuzziness and Knowledge Based Systems, 13 (6) (2005), 619 - 631.
Ganesan, K. On Some Properties of Interval Matrices, International Journal of Com- putational and Mathematical Sciences, 1 (2) (2007), 92-99.
Golub, Gane H., and Loan Charles F. Van. 1996. Matrix Computation Third Edition. United States of America: The Johns Hopkins University Press.
Hansen, E.R. and Smith, R.R. Interval arithmetic in matrix computations, Part 2, SIAM. journal of Numerical Analysis, 4 (1967), 1-9.
Hargreaves, Gareth I. 2002. Interval Analysis in Matlab. England: University of Manchester.
Harville, David A. 1997. Matrix Algebra From a Statistician's Perspective. New York : Springer-Verlag, Inc.
Kandasamy, Vasantha and Smarandance, Florentin. 2011. Algebraic Structures Us- ing Super Interval Matrices.
Kandasamy, Vasantha and Smarandance, Florentin. 2006. Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications. Phoenix: Hexis.
Kandasamy, Vasantha and Smarandance, Florentin. 2010. Interval Linear Algebra. Glendale: Kappa & Omega.
Kaucher, E. Interval Analysis in the Extended Interval Space . Computing, Suppl. 2 (1980), 33 - 49.
Lay, David C. 2006. Linear Algebra and Its Applications Third Edition Update. United States of America: Pearson Education, Inc.
Meyer, Carl D. 2000. Matrix Analysis and Applied Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics.
Moore, Ramon E., Kearfott, Ralph Baker and Cloud, Michael J. 2009. Introduction to interval analysis. Philadelphia: Society for Industrial and Applied Mathematics.
Neumaier, A. 1990. Interval Methods for Systems of Equations. United States of America: Cambridge University Press.
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.
Unduhan
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2014-08-14
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Abdullah, S., Warli, & Nurfalah, E. (2014). GENERALISASI METODE DEKOMPOSISI LU ( DOOLITTLE DAN CROUT ) DAN LDU UNTUK MENYELESAIKAN SISTEM PERSAMAAN MATRIKS INTERVAL. Prosiding Seminar Nasional Matematika Dan Pendidikan Matematika, 5(1), 437–450. Diambil dari http://prosiding.unirow.ac.id/index.php/snmpm/article/view/61
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