The AOR Iterative Method for Preconditioned Linear Systems

In Ref.[1], two preconditioned methods for linear system Ax = b (1) are introduced, where nnAC×∈ ,nb∈ C are given and nx ∈ C is unknown. It is given as the following preconditioned methods. The preconditioned linear system A~ x= b~ (2) where A~ = (I S~)A, and b~ = (I S~)b with S~=????????????? 000000001LMMMMLLna and the preconditioned linear system A =(3) 0where I is the identity matrix, L and U are strictly lower and upper triangular matrices obtained from A, respectively. The c…     

线性方程组预条件AOR迭代法注记

本文讨论了两类解线性方程组Ax=b的预条件方法,得到当经典AOR(SOR或Jacobi)迭代法收敛时,此类预条件AOR(SOR或Jacobi)迭代法也收敛且收敛速度较相应的经典方法快,而当经典AOR(SOR或Jacobi)迭代法发散时,此类预条件AOR(SOR或Jacobi)迭代法也发散。从而改进和完善了几个已有的结果。