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解一类对称不定线性方程组的奇异方向法

梁振珊   

  1. 吉林大学
  • 出版日期:1983-04-14 发布日期:1983-04-14

梁振珊. 解一类对称不定线性方程组的奇异方向法[J]. 计算数学, 1983, 5(4): 430-434.

THE SINGULAR DIRECTION METHOD FOR SOLVING A CLASS OF SYMMETRIC NONDEFINITE LINEAR SIMULTANEOUS EQUATIONS

  1. Liang Zhen-shan Jilin University
  • Online:1983-04-14 Published:1983-04-14
此处B为n×n对称正定矩阵,G是秩为m的n×m矩阵.这是在最优化问题和混合有限元法中大量出现的一类方程组,因此,它的求解问题引起人们的注意. 求解对称不定线性方程组问题已有较多讨论,但针对(2)中A的特殊性构造的算法尚
Let A be a matrix in form ,where B is a symmetric positive definite n×n matrix, G is a n×m matrix of rank m.In this paper, we find two groups singular vectors of A, which are conjugate each othar. By means of these vectors we constructe the singular direction method for solv-ing the system Ax = b. And the convergence of this method is demonstrated.
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[1] 曹维潞,关于一种特殊形状线性方程组的求解问题,计算数学,1(1978) ,74-79.
[2] D. G. Luenberger, Hyperbolic pairs in the method of conjugata gradients, SIAM, J. Appl. Math.,Vol. 17. No. 6. 1969, 1263-1267.
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