对称正定严格对角占优矩阵的预处理

Preconditioning of Strictly Diagonally Dominant Symmetric Definite Matrix

共轭梯度算法解大规模线性方程组的收敛速度依赖于矩阵的条件数．对正定严格对角占优矩阵、Ｍ－矩阵及Ｈ－矩阵给出了对称超松弛的修正预处理方法，并对预处理后的矩阵的条件数给出了估计式．

Much interest has been shown in the use of incomplete factorization of matrices in conjugation with applications of the generalized conjugate gradient method for approximate solutions to large sparse systems of linear equations. This paper presents a modified incomplete factorization for real symmetric positive definite strictly diagonally dominant matrix, Mmatrix, and Hmatrix (MSSOR method), and gives estimations of the condition number of the preconditioned matrices.