【摘要】 <正> 设线性方程组Ax=b,系数矩阵A=D-L-U或A=D-L-E-U,其中D非奇异。不妨设D=I,为讨论求解Ax=b的AOR法,EAOR法和TOR法的收敛性,[1—4]中分别给出了它们的迭代矩阵L_γω=（I-γL）^-1[（1-ω）I+（ω-γ）L +ωU],_γω=（I-γL）^-1[（γ-ω²）I+ω²U+（ω²-γ²）L]/γ,_αβq=（I-aL-βE）^-1[（1-q）I+（q-α）L+（q-β）E+qU],γ,ω,α,β,q∈R谱半径ρ（_γω）,ρ（_γω）和ρ（_γω）的上下界,[5]曾就一般迭代矩阵M（-1）N的谱半径ρ(M_-1N)的上下界,给出了下列结果:更多还原

【Abstract】 In this paper we give new results of the upper and lower bounds of the spectral radii of the iteration matrices αβq,yw,and Lyw of the TOR, AOR and EAOR iterative methods given in [4,1,3] respectively which are better than the previous results, and establish the convergence domains of the TOR iterative method, recover and extend the existing results of the AOR and EAOR iterative methods, for the strictly diagonally dominant matrix.更多还原