GAOR迭代法和Jacobi迭代法的敛散关系

Convergence and Divergence Relation between GAOR Method and Jacobi Method

中文关键词:  GAOR迭代法  Jacobi迭代法  收敛  发散

英文关键词:GAOR iterative method  Jacobi iterative method  convergence  divergence.

中文摘要:

      本文将文［１］中ＡＯＲ法和Ｊａｃｏｂｉ法同时敛散的结论推广到ＧＡＯＲ法．证明了当Ｊａｃｏｂｉ矩阵Ｂ非负时，解线性方程组Ａｘ＝ｂ（Ａ为不可约矩阵）的ＧＡＯＲ法（０≤γ_ｉ＜ω_ｉ≤１，ｉ＝１，２，…，ｎ）和Ｊａｃｏｂｉ法同时敛散，给出了其谱半径ρ（Ｌ_Ｒ，Ω）和ρ（Ｂ）之间的关系．

英文摘要:

      GAOR method and Jacobi method for solving system of linear equations are provedto be convergent and divergent simultaneously in case Jacobi matrix B is nonnegative.The relation between the spectral radius ρ(L_Ｒ，Ω)of GAOR iterative matrix and ρ(B) isdetermined.