New estimations of the spectral radii of J, G–S and SOR iterative matrices for a class of linear systems

Abstract

Given the linear system Ax=b, new upper bounds for the spectral radii of Jacobi, Gauss–Seidel and SOR iterative matrices are presented. Practical conditions of convergence for these iterations, which are suited to extended matrix classes containing strictly diagonally dominant matrices, are obtained.

Keywords:

• Linear systems
• Iteration
• Spectral radius
• Diagonal dominance

Acknowledgements

The authors would like to thank the referees very much for their detailed and helpful comments for revising this paper. The research reported in this paper was supported by NCET of the People’s Republic of China under grant number NCET-04-0893.