Block SOR methods for fuzzy linear systems

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.

The Mixed Type Splitting Methods for Solving Fuzzy Linear Systems

“…There are several well-known point iterative methods and block numerical iterative methods for FLS such as Jacobi, Gauss-Seidel, SOR, and AOR; see [9][10][11][12][13][14]. As a matter of fact, these methods are generalization of iterative methods for crisp linear systems = .…”

“…In [1,2] Kandel et al applied the embedding method for fuzzy linear system (hereafter denoted by FLS) and replaced the FLS by a 2 × 2 crisp linear system. This model has been modified later by some other researchers; see [10][11][12][13][14][15][16] and the references therein.…”

M-Preconditioner for Solving Fuzzy Linear Systems

“…. + a nn x n = y n , (1.1) where the coefficient matrix A = (a ij ) is a crisp matrix and y i is a fuzzy number, 1 6 i, j 6 n. Many authors study numerical methods for solving FLS (1.1), such as Abbasbandy, Ezzati and Jafarian [1][2][3]9], Allahviranloo [4][5][6], Dehghan and Hashemi [8], Fariborzi Araghi and Fallahzadeh [10], Li, Li, and Kong [14], Miao, Wang, Zheng, and Yin [15,[18][19][20][21], Nasser, Matinfar, and Sohrabi [16], and Zhu, Joutsensalo, and Hämäläinen [22]. Some applications lead to the linear system (1.1) with an M -matrix A. Hashemi, Mirnia, and Shahmorad [12] solved the fuzzy linear system whose coefficient matrix is an M -matrix by using the Schur complement.…”

Uzawa method for fuzzy linear system

“…where the coefficient matrix A = (a i j ) is a crisp matrix and y i is a fuzzy number, 1 i, j n. Many authors study numerical iterative methods for solving FLS (1.1), such as Abbasbandy [1,2], Allahviranloo [3,4,5], Dehghan and Hashemi [17], Fariborzi Araghi and Fallahzadeh [20], Miao, Wang and Zheng [22,25,26]. In this paper, an Uzawa method (cf.…”