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Abstract
The paper presents a type of tridiagonal preconditioners for solving linear system Ax=b with nonsingular M-matrix A, and obtains some important convergent theorems about preconditioned Jacobi and Gauss–Seidel type iterative methods. The main results theoretically prove that the tridiagonal preconditioners cannot only accelerate the convergence of iterations, but also generalize some known results.
Acknowledgements
The authors wish to express their thanks to Professor E.H. Twizell, Professor Choi-Hong Lai and the three anonymous referees for their helpful suggestions and comments, which improved our paper greatly. The work was supported by National Natural Science Foundation of China (10771168) and Natural Science Foundation of Shaanxi Province (2007A16).