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A family of higher-order convergent iterative methods for computing the Moore-Penrose inverse. (English) Zbl 06045802
The paper describes an iterative method for computing the Moore-Penrose inverse that is an extension of the Li and Li method. 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 30x30 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 Li and Li paper. 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:
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
15A09Matrix inversion, generalized inverses
65F10Iterative methods for linear systems
References:
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