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Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (3): 375-384.doi: https://doi.org/10.1007/s10483-012-1557-x

• 论文 • 上一篇    下一篇

Preconditioned iterative methods for solving weighted linear least squares problems

沈海龙1,2 邵新慧1 张铁1   

  1. 1. College of Sciences, Northeastern University, Shenyang 110004, P. R. China;
    2. College of Information Science and Engineering, Northeastern University, Shenyang 110004, P. R. China
  • 收稿日期:2011-10-10 修回日期:2011-12-14 出版日期:2012-03-02 发布日期:2012-03-01

Preconditioned iterative methods for solving weighted linear least squares problems

 SHEN Hai-Long1,2, SHAO Xin-Hui1, ZHANG Tie1   

  1. 1. College of Sciences, Northeastern University, Shenyang 110004, P. R. China;
    2. College of Information Science and Engineering, Northeastern University, Shenyang 110004, P. R. China
  • Received:2011-10-10 Revised:2011-12-14 Online:2012-03-02 Published:2012-03-01

PDF

1006

被引次数

15

摘要： A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation (GAOR) methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

Abstract: A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation (GAOR) methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

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