解实正定线性方程组的交替方向迭代法新格式

New form of the alternating direction iteration scheme for real positive definite linear systems

在许多适用于解实正定方程组的交替方向迭代法(Alternating Direction Iteration,ADI)的格式中,要求诸方向矩阵之间满足乘法可交换条件.这虽然可提高格式的效率,却也限制了ADI的应用范围.本文提出了一些修改的ADI格式(Revised Alternating Direction Iteration,RADI),免除可交换性的苛求,从而极大地扩充了ADI的应用范围.同时,本文还探讨了提高RADI格式效率的若干措施.

Alternating direction iteration(ADI)scheme is an effective method for solving real positive definite linear systems;in many cases,however,the method requires that all the direction matrices involved are multiplication exchangeable,which severely limits the scope of application.In this paper,new revised alternating direction iteration(RADI)schemes are proposed,that do not stipulate the multiplication exchangeable requirement,thereby expanding the application scope.In parallel,measures to improve the efficiency of RADI schemes are also discussed.