Abstract
In this paper, the block SOR iterative methods are studied for n×n fuzzy linear systems and the corresponding convergence theorems are also given out. We know that the coefficient matrix S of the augmented system SX=Y is consistently ordered when S 1 is nonsingular, and in this case the optimal parameter ω of the block SOR method is obtained. Numerical examples are presented to illustrate the theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Allahviranloo, T.: Numerical methods for fuzzy system of linear equations. Appl. Math. Comput. 155, 493–502 (2004)
Dehghan, M., Hashemi, B.: Iterative solution of fuzzy linear systems. Appl. Math. Comput. 175, 645–674 (2006)
Friedman, M., Ma, M., Kandel, A.: Fuzzy linear systems. Fuzzy Sets Syst. 96, 201–209 (1998)
Wang, K., Zheng, B.: Symmetric successive overrelaxation methods for fuzzy linear systems. Appl. Math. Comput. 175, 891–901 (2006)
Wang, K., Zheng, B.: Block iterative methods for fuzzy linear systems. J. Appl. Math. Comput. 25, 119–136 (2007)
Wu, C.-X., Ma, M.: Embedding problem of fuzzy number space: Part I. Fuzzy Sets Syst. 44, 33–38 (1991)
Young, D.M.: Iterative Solution of Large Linear Systems. Academic, New York (1971)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning. Inf. Sci. 8, 199–249, 301–357 (1975), 9, 43–80 (1975)
Zadeh, L.A.: Fuzzy sets as a basis for a possibility theory. Fuzzy Sets Syst. 1, 3–28 (1978)
Zheng, B., Miao, S.-X.: SAOR method for fuzzy linear system, J. Appl. Math. Comput. (accepted)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the Start-up foundation of Lanzhou University and the Natural Science Foundation of Gansu Province (3ZS051-A25-020), P.R. China. The third author was supported by China Postdoctoral Science Foundation (No. 20060400634).
Rights and permissions
About this article
Cite this article
Miao, SX., Zheng, B. & Wang, K. Block SOR methods for fuzzy linear systems. J. Appl. Math. Comput. 26, 201–218 (2008). https://doi.org/10.1007/s12190-007-0019-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-007-0019-y