论L_ω敛散性的新定理

On the New Theorem of the Convergence and Divergence of L_ω

本文论证了关于Jacobi矩阵B=L-U(L,U是非负阵)的逐次松弛矩阵的敛散性依赖于矩阵L+U。并给出了估计松弛矩阵之谱半径上下界的不等式。由此,还可证得对一般Jacobi矩阵B之松弛矩阵有:当|B|的谱半径小于1,则该松弛矩阵的谱半径小于1(这里松弛因子是在0和大于1的数C之间)。

For the successive relaxation matrix of Jacobi matrix B=L-U(L,U are nonegative matri- ces),this paper demonstrates that its convergence and divergence depend upon matrix L+U,and gives the inequalities for estimating upper and lower bounds of spectral radius in relaxation matrix.For the successive relaxation matrix of common Jacobi matrix B,this paper demonstrates that in case the spec- tral radius of |B| is less than 1,that of relaxation matrix will also be less than 1.Here the relaxation factor is in the range of 0 and C,a number greater than 1.