M-Preconditioner for Solving Fuzzy Linear Systems

Abstract

An M -preconditioner is provided for solving fuzzy linear systems whose coefficient matrices are crisp M -matrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the M -preconditioned conjugate gradient ( M PCG) method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

New Splitting Iterative Method for Fuzzy Linear Systems

“…According to Du, Zheng andWang's new iterative methods for linear systems [5], the following iterative scheme can be established for fuzzy linear system (1), i.e., (3)…”

“…Subsequently, lots of numerical methods were investigated for FLS (1) by a large number of authors, such as Abbasbandy, Ezzati and Jafarian [1], Allahviranloo [2], Dai, S. Wang and K. Wang [3], Dehghan and Hashemi [4], Fariborzi Araghi and Fallahzadeh [6]. In this paper, a new splitting iterative method is presented for FLS (1), compared with Jacobi method.…”