【摘要】 本文讨论线性方程组定常块二级迭代法内迭代次数的选择.对于单调矩阵,证明了块Jacobi矩阵的谱半径ρp（T）为非定常块二级迭代法R₁-因子的下界.对于M-矩阵,用某个单调范数给出了ρ（T_p）的关于p单调下降且收敛于ρ（T）的上界.于是,当系数矩阵为M-矩阵时,我们定义了定常块二级迭代法的近似最优内迭代次数.所定义的近似最优值与模型问题数值计算的实际最优值非常吻合.本文分析表明,实际计算中应该把内迭代次数控制在较小的数目.更多还原

【Abstract】 This article discusses the selection of the number of inner iterations of stationary block two-stage iterative methods for linear systems.It is shown that,for monotone matrices,the spectral radiusρ（T） of block Jacobi iteration matrix is the low bound of R₁-factor of the non-stationary block two-stage iterative methods.We apply a certain monotone norm to find out the decreasing upper bounds ofρ（T_p）,these upper bounds converge toρ（T） with p for M- matrices.Consequently,when coefficient matrices are M-matrices we define the approximate optimal number of the inner iterations for stationary block two-stage iterative methods;the approximate optimum defined very tallies with the real optimum of the numerical instance for model problem.It is deduced from our analysis that small number of inner iterations should always be used in applications.更多还原