(I+S_(max))预条件Gauss-Seidel迭代法进一步探索  

Further Study on (I+S_(max)) Preconditioning Gauss-Seidel Iterative Method

作　　者：庄伟芬[1] 卢琳璋[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2004年第B08期349-352,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10271099)资助

摘　　要：Kotakemori研究了不可约对角占优Z 阵的(I+Smax)预条件Gauss Seidel迭代法,并证明在一定条件下,进行(I+Smax)预处理比(I+S)预处理收敛效果更好.本文将其收敛性定理推广到具有广泛应用背景的H 阵,并将这两类预条件Gauss Seidel迭代法相结合对不可约非奇M 阵进行两次适当的预处理,数值例子表明这样可以大大加快Gauss Seidel迭代法的收敛速度.Hisashiki Kotakemori had proposed a preconditioner (I+S_(max)) for irreducibly diagonally dominant Z-matrix, which achieves better convergence rate than the classical Gauss-Seidel method and even better than Modified Gauss-Seidel method with preconditioner (I+S) under certain circumstances. We extend his convergence theorem to the case of H-matrix, and apply the preconditioner (I+S_(max)) to twice preconditioning for irreducible non-singular M-matrix, combining with another preconditioner (I+S). Numerical examples had been given to confirm that the convergence rate had been improved on considerably.

关 键 词：预条件Gauss-Seidel迭代法 收敛速度 H-矩阵 收敛性定理 线性方程组 

分 类 号：O241.6[理学—计算数学]