Linear system with M-matrices often appear in a wide variety of areas. In this work, we propose a new preconditioner for solving the system with nonsingular M-matrix. We show that our preconditioner increases the convergence rate of basic iterative methods. We also give a comparison between preconditioners with different parameters. Numerical results are also given.

In this paper, a new preconditioned AOR iterative method is proposed with the preconditioner I + Sα. Some comparison theorems are given when the coefficient matrix A of linear system is an irreducible L− matrix. Numerical example shows that our methods are superior to the basic AOR iterative method.

A preconditioned AOR iterative method is proposed with the preconditioner I + S∗ αβ. Some comparison theorems are given when the coefficient matrix of linear system A is an irreducible L−matrix. The convergence rate of AOR iterative method with the preconditioner I + S∗ αβ is faster than the convergence rate with the preconditioner I + Sα by Li et al. Numerical example verifies comparison theor...

Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Converg...

A preconditioned AOR iterative method is proposed with the preconditioner I + S∗ αβ. Some comparison theorems are given when the coefficient matrix of linear system A is an irreducible L−matrix. The convergence rate of AOR iterative method with the preconditioner I + S∗ αβ is faster than the convergence rate with the preconditioner I + Sα by Li et al. Numerical example verifies comparison theor...

Both Evans et al. and Li et al. have presented preconditioned methods for linear systems to improve the convergence rates of AOR-type iterative schemes. In this paper, we present a new preconditioner. Some comparison theorems on preconditioned iterative methods for solving L-matrix linear systems are presented. Comparison results and a numerical example show that convergence of the precondition...

In this paper we present a variant of the Accelerated Overrelaxation iterative method (AOR), denoted by modified AOR-like method (MAOR-like method) for solving the augmented systems, i.e. the AOR-like method with three real parameters , r and . For special values of r ,  and  we get the MSOR-like method, the AOR-like method and the SOR-like method. An equation relating the involved paramete...

In this paper, we derive an implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations, based on the Caputo’s time fractional derivative. Then this approximation equation leads the corresponding system of linear equation, which is large scale and sparse. Due to the characteristics of the coefficient matrix, we use the Accelerated Over-Rel...