Improvements of preconditioned AOR iterative method for L-matrices

In this paper, we improve the preconditioned AOR method of linear systems considered by Evans et al. [The AOR iterative method for new preconditioned linear systems, Comput. Appl. Math. 132 (2001) 461–466]. In Evans’ paper, the coefficient matrix of linear system have to be an L-matrix with a i , i + 1 a i + 1 , i > 0 , i = 1 , … , n - 1 and 0 < a 1 n a n 1 < 1 . When a i , i + 1 a i + 1 , i = 0 for some i ∈ N = { 1 , … , n - 1 } , the preconditioned method is invalid. In order to solve the above problem, a new preconditioner is presented. Meanwhile, some recent results are improved.