【摘要】 设A∈Cn×n是2-循环相容次序阵,其Jacobi阵J的非零特征值均为纯虚数.记α=ρ(J).本文证明了A的AOR迭代阵Lr,ω(约定ω>0,r≠0)收敛当且仅当参数ω,r满足条件0<ω<21+α2,ω+ωα-22<r<12ω+(2ω-αω2)2,r≠0,或等价地,r≥rb,0<ω<2+rα2-α1+αr22α2+4r-4;rb≥r>-α22,r≠0,0<ω<21++rαα22,其中rb=1+21+α2.这一结果纠正了薛秋芳文给出的相应结果,并指出了其中的3个问题.更多还原

【Abstract】 Suppose A∈Cn×n is an 2-cyclic consistently ordered matrix and its non-zero eigenvalues of Jacobi matrix J has only pure imaginary.Set α=ρ(J).In this paper we prove that the AOR iteration matrix Lr,ω(with ω>0 and r≠0) of A converges iff0<ω<2 1+α2,ω+ω-2 α2<r<1 2[ω+(2-ω)2 ωα2],r≠0,or equivalently,{r≥rb,0<ω<2+rα2-αr2α2+4r-4 1+α2;rb≥r>-2 α2,r≠0,0<ω<2+rα2 1+α2,where rb=2 1+1+α2.This result corrects the corresponding one obtained by Xue.更多还原