The upper bound of the spectral radius of M^-1 N and convergence of some iterative methods

Abstract

Using a concise method, different from those in [1-3,7,8] used by K. R. James, M. Martins and Hu Jia-gan, repectively, this paper discusses the upper bounds of the spectral radii of the matarices M^-1N and Lyoi which is the AOR type matrix, and gives new results. Based on these conclusions further results for the convergence domains of the AOR and GAOR, SOR and GSOR iterative methods with strictly or irreducibly diagonally dominant matrices are obtained. Finally conditions equivalent to the statement that the matrix is strictly or irreducibly diagonally dominant by rows are established.

Keywords:

• Upper bound
• Spectral radius
• Convergence domain
• AOR and GAOR iterative methods
• SOR and GSOR iterative methods
• strict or irreducible diagonal dominance