Chebyshev Acceleration Technique for Solving Fuzzy Linear System
محورهای موضوعی : Data Envelopment Analysis
1 - Department of Mathematics, University of Mazandaran, Babolsar, Iran.
2 - Department of Mathematics, University of Mazandaran, Babolsar, Iran.
کلید واژه: ACCELERATION TECHNIQUES, CHEBYSHEV ACCELERATION TECHNIQUE, Fuzzy system of linear equations, Iterative methods,
چکیده مقاله :
In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS). This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.
In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS). This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.
[1] Abbasbandy S., Ezzati R., and Jafarian A., LU decomposition method for solvingfuzzy system of linear equations, Applied Mathematics and Computation, 172, 633-643, 2006.
[2] Allahviranloo T., Numerical methods for fuzzy system of linear equations, Applied Mathematics and Computation, 155, 493-502, 2004.
[3] Allahviranloo T., Successive overrelaxation iterative method for fuzzy system of linear equations, Applied Mathematics and Computation, 162, 189-196, 2005.
[4] Allahviranloo T., The adomian decomposition method for fuzzy system of linear equations, Applied Mathematics and Computation, 163, 555-563, 2005.
[5] Chang S. S. L., and Zadeh L. A., On fuzzy mapping and control, IEEE Trans. System Man. Cybernet., 2, 30-34, 1972.
[6] Cong-xin W., and Ming M., Embedding problem of fuzzy number Space: Part I, Fuzzy Sets and Systems, 44, 33-38, 1991.
[7] Datta B. N., Numerical Linear Algebra and Applications, ITP Press, New York, 1995.
[8] Dehghan M., Hashemi B., Iterative solution of fuzzy linear systems, Applied Mathematics and Computation, 175, 645-674, 2006.
[9] Friedman M., Ming M., and Kandel A., Fuzzy linear systems, Fuzzy Sets and Systems, 96, 201-209, 1998.
[10] Golub G. H., and Van Loan C. F., Matrix Computations, 3rd edition, The Johns Hopkins University Press, 1996.
[11] Luenberger D. G., and Ye Y., Linear and Nonlinear Programming, 3rd edition, Springer, 2008.
[12] Matinfar M., Nasseri S. H., and Sohrabi M., Solving fuzzy linear system of equations by using Householder decomposition method, Applied Mathematical Sciences, 52, 2569-2575, 2008.
[13] Nasseri S. H., and Khorramizadeh M., A new method for solving fuzzy linear systems, Inter. J. Appl. Math., 20 No. 4, 507-516, 2007.
[14] Nassei S. H., Solving fuzzy linear system of equations by use of the matrix decomposition, Inter. J. Appl. Math., 21, 435-445, 2008.
[15] Nassei S. H., and M. Sohrabi, Solving fuzzy linear systems: based on the degree of membership, Inter. J. Appl. Math., 22(1), 89-101, 2009.
[16] Zadeh L. A., The concept of linguistic variable and its application to approximate reasoning, Inform. Sci., 8, 199-249, 1975.
