块AOR、块SOR和块JOR迭代法的收敛性

CONVERGENCE OF THE BLOCK AOR, SOR AND JOR ITERATIVE METHODS

本文引进块Jacobi迭代矩阵B的优矩阵(?),来研究解线性方程组的块AOR、块SOR和块JOR迭代法的收敛性。即若‖·‖是矩阵的某个相容范数。且‖B_(ij)‖(?)β_(ij),i,j=1,…,m,则令(?)=(β_(ij))。利用(?),我们给出了块AOR(0(?)γ<2/[1+ρ(?)]),0<ω<max(2γ/[1+ρ(Lγ)],2/[1+ρ(?)]),块SOR(0<ω<2/[1+ρ(?)])和块JOR(0<ω<2/[1+ρ(?)]迭代法收敛的若干充分条件。

In this paper, we discussed convergence of the block AOR, SOR and JOR iterative methods for solving systems of linear equations. Let B be block Jacobi matrix, we defined its control matrix, i. e. ‖B_(ij)‖;<;β_(ij) i, j=1, …, m, for some matrix norm and =(β_(ij)). Using, some sufficient conditions of convergence of block AOR(0≤γ<2/[1+ρ], 0 <ω<max(2γ/[1+ρ(L_7)], 2/[1+ρ])), SOR (0<ω<2/[1+ρ])and JOR (0<ω<2/[1+ρ])iterative methods are given.