Convergence of the generalized AOR method

摘要

A generalized AOR (GAOR) method is proposed here to solve the linear system with some special structure. The convergence of the GAOR method is studied. The convergence result obtained here is an extension of the classical convergence result of the regular AOR method with weaker condition. In comparing with the generalized SOR (GSOR) method, we show that the GAOR method is better than the GSOR method under certain conditions. In some cases, the GAOR method is convergent even if the GSOR method does not converge. Finally, the GAOR method is applied to solve the generalized least-squares (LS) problems. Three numerical algorithms for the generalized LS problems are given.