解线性代数方程组的TCG迭代法

ICCG方法是解线性代数方程组较为理想的方法,但它仅适用于具有正定对称的系数阵。本文介绍的TCG方法便足改造过的ICCG方法,它适用于一般非奇异的非正定对称阵。TCG方法比常用的JLUCG方法,对于非定常问题,可提高效率18%,特别是取用SIP不完全L、U分解作预条件时,可提高效率40%,是计算非正定对称阵较为理想的迭代法之一。本文推导出在消去法不完全L,U分解下的TCG方法,并用数值结果论证出它比ILUCG方法加速收敛的所在。

TCG ITERATIVE METHOD FOR SOLVING SYSTEM OF LINEAR ALGEBRAIC EQUATIONS

The method ICCG. is one of the best iterative method for solving the system of linear algebraic equations, but it can only be applied to the symmetric and positive definite coefficient matrix. The TCG method itroduced in this paper is a modified ICCG mothod. It can be applied to the matrices which are non-singular、unsymmetric and not positive definite. For the unsteady problem this method can raise the efficiency by 18 percent as compared with tie ILU.CG method. In particular if we take the SIP incomplete L、U decomposition as the preconditioned method, TCG method can raise the efficiency by 40 percent. It is indeed a bast iterative method applied to the matrices which are unsymmetric and not positive definite. In this paper we deduce the TCG method with the elimination method as the incomplete L、U decomposition and use the computational results to indicate the reason why the TCG method converges more quickly than ILUCG method.