A family of iterative methods for computing Moore-Penrose inverse of a matrix

作者：Li Weiguo^*; Li Juan; Qiao Tiantian

来源：Linear Algebra and Its Applications, 2013, 438(1): 47-56.

DOI：10.1016/j.laa.2012.08.004

• Moore-Penrose inverse
• Inner inverse
• Iterative method
• R-Convergence

This paper improves on generalized properties of a family of iterative methods to compute the approximate inverses of square matrices originally proposed in [1]. And while the methods of [1] can be used to compute the inner inverses of any matrix, it has not been proved that these sequences converge (in norm) to a fixed inner inverse of the matrix. In this paper, it is proved that the sequences indeed are convergent to a fixed inner inverse of the matrix which is the Moore-Penrose inverse of the matrix. The convergence proof of these sequences is given by fundamental matrix calculus, and numerical experiments show that the third-order iterations are as good as the second-order iterations.

• 出版日期2013-1-1
• 单位中国石油大学（北京）