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 _ai,i+1ai+1,i>0$a_{i,i+1}{a}_{i+1,i}>0$, i=1,…,n-1$i=1,\dots ,n-1$ and 0<_a1nan1<1$0<a_{1n}{a}_{n1}<1$. When _ai,i+1ai+1,i=0$a_{i,i+1}{a}_{i+1,i}=0$ for some i∈N={1,…,n-1}$i\in N=\{1,\dots ,n-1\}$, the preconditioned method is invalid. In order to solve the above problem, a new preconditioner is presented. Meanwhile, some recent results are improved.