Note on Irreducible Diagonally Dominant Matrices and the Convergence of the AOR Iterative Method

A note on nonnegative diagonally dominant matrices

A note on the convergence of the AOR method

In Gao and Huang [Z.X. Gao, T.Z Huang, Convergence of AOR method, Appl. Math. Comput. 176 (2006) 134–140] some practical sufficient conditions for the convergence of the AOR (accelerated overrelaxation) method for solving linear system Ax 1⁄4 b, with A being doubly diagonally dominant matrix, are presented. Using a different approach we will give some improvements in both cases, when the matrix...

Convergence of GAOR Iterative Method with Strictly α Diagonally Dominant Matrices

Guangbin Wang, Hao Wen, and Ting Wang Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China Correspondence should be addressed to Guangbin Wang, [email protected] Received 11 June 2011; Revised 20 September 2011; Accepted 22 September 2011 Academic Editor: Yongkun Li Copyright q 2011 Guangbin Wang et al. This is an open access article distributed ...

A note on the convergence of the generalized AOR iterative method for linear systems

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...

Improving AOR Iterative Methods For Irreducible L-matrices

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...