块TOR迭代法的收敛性

Convergence of block TOR iterative methods

基于弱块对角占优矩阵与弱块H矩阵理论,利用最优尺度矩阵的方法给出了块TOR迭代法(BTOR迭代法)的收敛准则、迭代矩阵谱半径的上界估计式:若A为弱块H矩阵理论,则当α≥0,β≥0且0<α+β<4/[1+ρ(|^J(A)|]时,A的块TOR迭代法迭代矩阵谱半径满足:ρ(^Lα,β,F(A))≤|1-α+β2ρ(|^J(A)|)。

By the theory of weak block diagonally dominant matrices and weak block H -matrices,the block two-parameter overrelaxation (BTOR) methods are present, which generalized the TOR iterative methods for the solution of large linear systems.The convergence of BTOR iterative methods and some estimations about the spectral radius about BTOR methods are investigated in case that A is a weak block H -matrix:if α≥0,β≥0, and 0<α+β<4/, then ρ( _(α,β,F)( A ))≤|1-α+β 2|+α+β 2ρ(| (A )|).