东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2012, Vol. 33 ›› Issue (8): 1213-1216.DOI: -

• 论著 • 上一篇    

求解H-矩阵线性方程组的预处理Gauss-Seidel方法

邵新慧;沈海龙;张铁;   

  1. 东北大学理学院;东北大学信息科学与工程学院;
  • 收稿日期:2013-06-19 修回日期:2013-06-19 发布日期:2013-04-04
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(11071033);;

Preconditioning Gauss-Seidel methods for the solution of H-matrices systems

Shao, Xin-Hui (1); Shen, Hai-Long (1); Zhang, Tie (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110819, China; (2) School of Information Science and Engineering, Northeastern University, Shenyang 110819, China
  • Received:2013-06-19 Revised:2013-06-19 Published:2013-04-04
  • Contact: Shen, H.-L.
  • About author:-
  • Supported by:
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摘要： 针对系数矩阵A为H-矩阵,为线性方程组Ax=b引入了两种形式的预处理矩阵I+-S和I+S^,给出了相应的预处理Gauss-Seidel方法.证明了若系数矩阵A为H-矩阵,则新的系数矩阵(I+-S)A和(I+S^)A仍是H-矩阵,并给出了相应预条件Gauss-Seidel方法的收敛性分析.通过数值算例验证了新的预处理迭代方法的收敛率比经典的Gauss-Seidel迭代法以及J.P.Milaszewicz提出的改进Gauss-Seidel迭代法更好.

关键词: H-矩阵, 线性方程组, Gauss-Seidel方法, 预处理矩阵, 收敛率

Abstract: For the linear equations Ax=b, two new preconditioning matrices I+S¯ and I+Sˆ were introduced, and corresponding Gauss-Seidel methods were obtained. It was proved that if the coefficient matrix A of the original system was an H-matrix, then the coefficient matrices (I+S¯)A and (I+Sˆ) A of the preconditioning system were also an H-matrix. The convergence theorems of the new methods were proposed. Finally, numerical example was carried out and the results indicated that the convergence rates of the new preconditioning methods are better than those of the corresponding classical Gauss-Seidel method and the modified Gauss-Seidel method proposed by J. P. Milaszewicz.

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