## A family of higher-order convergent iterative methods for computing the Moore-Penrose inverse.(English)Zbl 1298.65068

The paper describes an iterative method for computing the Moore-Penrose inverse that is an extension of the method by W. Li and Z. Li [ibid. 215, No. 9, 3433–3442 (2010; Zbl 1185.65057)]. The paper is short, well-written, and relatively clear. It contains basic concept of the method, three auxiliary lemmas, and the main theorem proving the convergence. The promising numerical experiments are performed for at most $$30\times 30$$ matrices. On the other hand, not all is written in the paper. To understand some parameters of the basic iterative scheme, it is necessary to see the original paper by Li and Li. It seems also that the method is not suitable for large-scale problems, since each iteration requires multiplications of matrices – the time consuming operation.

### MSC:

 65F20 Numerical solutions to overdetermined systems, pseudoinverses 15A09 Theory of matrix inversion and generalized inverses 65F10 Iterative numerical methods for linear systems

### Keywords:

Moore-Penrose inverse; iterative method; convergence rate

Zbl 1185.65057
Full Text:

### References:

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