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J4 ›› 2009, Vol. 44 ›› Issue (10): 30-35.

• 论文 • 上一篇    下一篇

亏秩线性方程组的PSD迭代解法

岳强 畅大为   

  1. 陕西师范大学数学与信息科学学院,陕西 西安 710062
  • 收稿日期:2009-03-16 出版日期:2009-10-16 发布日期:2009-12-07
  • 通讯作者: 畅大为(1963),男,副教授,主要从事数值线性代数的研究.
  • 作者简介:岳强(1984),男,硕士,主要从事数值线性代数的研究.Email:yqttt@163.com
  • 基金资助:

    国家自然科学基金资助项目(60671063)

Preconditioned simultaneous displacement(PSD) method for rank deficient  linear systems

 YUE Jiang, CHANG Da-Wei   

  1. College of Mathematics and Information Science, Shaanxi Normal University,Xi an 710062, Shaanxi, China
  • Received:2009-03-16 Online:2009-10-16 Published:2009-12-07

摘要:

将亏秩线性方程组Ax=b增广为以方阵Â为系数矩阵的4×4块线性方程组Âη=b´,再对A进行次正则PSD分裂,得到PSD迭代法半收敛的一个充要条件。最后给出求方程组Ax=b范数最小的最小二乘解的方法并以实例说明, 其中A∈Cm×n,b∈Cm,b´∈C m+n

关键词: PSD分裂;半收敛;最小二乘解;Moore Penrose广义逆

Abstract:

The rank deficient linear systemÂx=b  is augmented to a block 4×4 linear system Âη=b´, where A is a square matrix, then A is split with PSD subproper splitting. The necessary and sufficient condition for the PSD method being semiconvergent is obtained. Finally a method is provided to compute the least square solution of minimal norm to ]Ax=b and exmamples are given to illustrate the process, whereA∈Cm×nb∈Cm,b´∈C m+n

Key words: PSD splitting; Semiconvergent; Least square solution; Moore-Penrose generalized inverse

中图分类号: 

  • Q241.6
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