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Abstract
The concept of strictly β-diagonally dominant matrices is introduced. This concept is directly related to solving a system of equations. In the linear case, the strictly β -diagonally dominant matrices contain the strictly diagonally dominant matrices. However, for systems of nonlinear equations, it is a challenge to present a better condition to make sure that the iteration algorithm used to solve them is convergent. A new class of nonlinear mappings and some properties are offered; moreover, the corresponding convergence theorems of the nonlinear Gauss–Seidel and Jacobi iterations are presented.
Acknowledgements
The authors would like to thank the referees for their valuable comments and suggestions. This work was supported by NCET of the Chinese Ministry of Education (NCET-04-0893), the scientific and technological key project of the Chinese Ministry of Education (107098), the Sichuan province foundation for applied basic research (05JY029-068-2) and project for academic leader + group of UESTC.