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计算Moore-Penrose广义逆矩阵的一种直接方法

林应举   

  1. 南京大学计算中心
  • 出版日期:1981-02-20 发布日期:1981-02-20

林应举. 计算Moore-Penrose广义逆矩阵的一种直接方法[J]. 数值计算与计算机应用, 1981, 2(2): 94-97.

A DIRECT METHOD OF COMPUTING THE MOORE-PENROSE INVERSE OF A MATRIX

  1. Lin Ying-ju Computing Centre, Nanjing University
  • Online:1981-02-20 Published:1981-02-20
计算一个m×n(m≥n)矩阵A的M-P广义逆A~+的一类直接方法,是将A进行QU分解:
In this paper, for computing the Moore-Penrose inverse of an m×n matrix A, whenrank (A) = r< n and n - r is small, we suggest that ofter decompositing A into QU,U~+ is computed by use of Graville's recursive algorithm, and then A~+ is obtained. Inaddition, according to the generalization made by cline for the Graville's method, thecorresponding representation is given and applied it to compute the minimal least squaresolution of a system of linear equations.
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[1] T. N. E. Graville, Some applications of the pesudo inverse of a matrix, SIAM Rev., 2, 1960, 15-22.
[2] R. E. Cline, Representations for the generalized inverse of a partioned matrix, JSIAM, 12, 1964, 588-600.
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