Global relaxed non-stationary multisplitting multi-parameter methods

Abstract

Based on the local relaxed method and the system relaxed method of parallel multisplitting described by Frommer and Mayer, the paper presents a global relaxed non-stationary multisplitting multi-parameter method by introducing some relaxed parameters. Convergence of these methods when coefficient matrices are H-matrices is investigated. Efficiency of the global relaxed non-stationary multisplitting multi-parameter method is shown by numerical experiments. These indicate that, when choosing the approximately optimal relaxed parameters, the methods have a faster convergent rate than previous methods.

Keywords:

• Relaxed non-stationary multisplitting multi-parameter method
• Parallel multisplitting
• Global relaxed method
• H-matrix

Acknowledgements

The authors would like to thank the referees and editor for their helpful and detailed suggestions for revising this manuscript. Supported by NCET of Chinese ministry of education (NCET-04-0893), scientific and technological key project of Chinese ministry of education (107098), Sichuan province foundation for applied basic research and leader of sci. and tech. and project for academic leader and group of UESTC.