GAOR迭代法的收敛性

当A为实对称矩阵时,1]中在D_i选取较特殊的条件下,证明了GAOR迭代法收敛的充要条件为A是正定矩阵. 设A为Hermite矩阵,进一步讨论GAOR迭代法收敛的充要条件. 以下记 B=D_1~(-1)(C_L+C_U).

ON THE CONVERGENCE OF GAOR METHODS

In 1] the generalized accelerated overrelaxation (GAOR) methods were proposed, whichgeneralized the basic iterative methods for the solution of linear systems. This paper investiga-tes the convergence of the GAOR methods. A number of new results are presented concern-ing the convergence theory of the GAOR methods and their special cases. Much attention isgiven to linear systems whose coefficient matrices are positive definite, and are L-matrices andH-matrices, respectively.