L-矩阵的预条件方法及其比较定理

Preconditioned methods of L matrices and its comparison theorems

给出了解线性方程组Ax=b的预条件Guass-Seidel法,讨论了对于不可约的L-矩阵应用这种方法的收敛性并得到了比较定理.此外,给出了收敛最快时的系数取值.通过数值例子说明该文提出的预条件Guass-Seidel法是有效的.

The preconditioned Guass - Seidel method for solving the linear system Ax = b is presented and the convergence of the preconditioned method applied to irreducible L matrices is discussed, and some comparison theorems are obtained. Besides, the optimal parameters are given and some numerical examples illustrate its validity.