2012 Volume 4 Pages 41-44
The Jacobi preconditioner is well known as a preconditioner with high parallel efficiency to solve very large linear systems. However, the Jacobi preconditioner does not always show the great improvement of the convergence rate, because of the poor convergence property of the Jacobi method. In this paper, in order to improve the quality of the Jacobi preconditioner without loss its parallel efficiency, we introduce a weighted Jacobi-type preconditioner, and propose an optimization technique for the weight parameter. The numerical experiments indicate that the proposed preconditioner has higher quality and is more efficient than the traditional Jacobi preconditioner.