Block Jacobi two-stage method with Gauss-Seidel inner iterations for fuzzy system of linear equations. (English) Zbl 1093.65032

Summary: We study a block two-stage iterative method for finding the approximate solution of fuzzy systems of linear equation with convergence conditions. The application of this method is solving large linear systems on parallel computer. The algorithm is illustrated by solving some numerical examples.


65F10 Iterative numerical methods for linear systems
08A72 Fuzzy algebraic structures
65Y05 Parallel numerical computation
Full Text: DOI


[1] Bukley, J. J., Fuzzy eigenvalue and input-output analysis, Fuzzy Sets Syst., 34, 187-195 (1990) · Zbl 0687.90021
[2] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci., 8, 199-249 (1975) · Zbl 0397.68071
[3] Friedman, M.; Ming, M.; Kandel, A., Fuzzy linear systems, FSS, 96, 201-209 (1998) · Zbl 0929.15004
[4] Diamond, P., Fuzzy least squares, Inform. Sci., 46, 144-157 (1988) · Zbl 0663.65150
[5] Allahviranloo, T., Numerical methods for fuzzy system of linear equations, Appl. Math. Comput., 155, 493-502 (2004) · Zbl 1067.65040
[6] Allahviranloo, T., Successive over relaxation iterative method for fuzzy system of linear equations, Appl. Math. Comput., 162, 189-196 (2005) · Zbl 1062.65037
[7] Allahviranloo, T., The Adomuan decomposition method for fuzzy system of linear equations, Appl. Math. Comput., 163, 553-563 (2005) · Zbl 1069.65025
[8] Cao, Z., Convergence of nested iterative methods for symmetric \(p\)-regular splittings, SIAM J. Matrix Anal. Appl., 22, 20-32 (2000) · Zbl 0978.65020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.