预优矩阵及其构造技术  

PRECONDITIONED MATRIX AND ITS STRUCTURE TECHNIQUE

作　　者：范啸涛[1] 季光明[1] 

机构地区：[1]成都理工大学信息管理学院,成都610059

出　　处：《成都理工大学学报（自然科学版）》2003年第4期432-435,共4页Journal of Chengdu University of Technology: Science & Technology Edition

摘　　要：为达到预处理共轭梯度法 ( PCG)提高收敛速度 ,克服数值不稳定性目的 ,给出了构造预优矩阵的条件 ,并构造了三个典型的预优矩阵。它们是不完全 Cholesky因子预优矩阵 ,对角预优矩阵和利用 SSOR法导出的预优矩阵 ,且在 PCG中是应用效果很好的预优矩阵。In order to make the preconditioned conjugate gradient method(PCG) increase the convergence speed and overcome the number unstability, this paper gives the conditions to structure the preconditioned matrix and structure the three typical preconditioned matrixes. They are the preconditioned matrix with the incompletely Cholesky factor, the diagonal preconditioned matrix, and the preconditioned matrix induced by SSOR. They are effective preconditioned matrixs in PCG.

关 键 词：条件数 预处理共轭梯度法 不完全Cholesky分解 对称逐次超松弛迭代法 

分 类 号：O242.2[理学—计算数学]