A family of iterative methods for computing Moore-Penrose inverse of a matrix. (English) Zbl 1258.65035

Weiguo, Li; Juan, Li; Tiantian, Qiao

Linear Algebra Appl. 438, No. 1, 47-56 (2013).

Summary: This paper improves on generalized properties of a family of iterative methods to compute the approximate inverses of square matrices originally proposed in [the author and Z. Li, Appl. Math. Comput. 215, No. 9, 3433–3442 (2010; Zbl 1185.65057)]. And while the methods of [loc. cit.] 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.

MSC:

65F20

Numerical solutions to overdetermined systems, pseudoinverses

Keywords:

Moore; Penrose inverse; inner inverse; iterative method; R-convergence

Citations:

Zbl 1185.65057

References:

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