Z-矩阵的预处理迭代方法

对解大型稀疏线性方程组Ａｘ＝ｂ，当其系数矩阵Ａ为严格对角占优的Ｚ 矩阵时给出了一种预处理方法，证明了预处理后的矩阵Ａｐ的Ｇａｕｓｓ－Ｓｅｉｄｅｌ及对称的Ｇａｕｓ－Ｓｅｉｄｅｌ迭代均是收敛的，并且对Ｇａｕｓ－Ｓｅｉｄｅｌ迭代的迭代矩阵ＴＤ的谱半径ρ（Ｔｐ）给出了一个上界．同时也证明了对Ｇａｕｓ－Ｓｅｉｄｅｌ迭代法而言，经预处理后的迭代法优于经典的直接迭代法．

The Iterative Method for Preconditioned ZMatrix

A preconditioning method of the coefficient matrix BXA, which is a strictly diagonally dominant Zmatrix, of large-scale sparse linear equation AX=b is put forward. It is proven that Gauss-Seidel iteration and symmetrical Gauss-Seidel iteration of the preconditioned A p matrix are convergent, and that the preconditioned Gauss-Seidel iteration method is superior to classical Gauss-Seidel iteration method. At the same time, a upper bound of ( T p) of iteration matrix T p is given.