Article

New preconditioned AOR iterative method for Z-matrices

Journal of Applied Mathematics and Computing 05/2012; 37(1):103-117. DOI:10.1007/s12190-010-0423-6 pp.103-117

ABSTRACT In this paper, we present a new preconditioned AOR-type iterative method for solving the linear system Ax=b, where A is a Z-matrix, and prove its convergence. Then we give some comparison theorems to show that the rate of convergence of the In this paper, we present a new preconditioned AOR-type iterative method for solving the linear system Ax=b, where A is a Z-matrix, and prove its convergence. Then we give some comparison theorems to show that the rate of convergence of the
preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method. Finally, preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method. Finally,
we give two numerical examples to illustrate our results. we give two numerical examples to illustrate our results.

KeywordsZ-matrix–AOR-type iterative method–Precondition–Comparison theorem–Linear system KeywordsZ-matrix–AOR-type iterative method–Precondition–Comparison theorem–Linear system

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Keywords

AOR-type iterative method
 
comparison theorems
 
convergence
 
new preconditioned AOR-type iterative method
 
numerical examples
 
preconditioned AOR-type iterative method
 
Z-matrix