Further representations and computations of the generalized Moore-Penrose inverse

Kezheng Zuo; Yang Chen; Li Yuan; Kezheng Zuo; Yang Chen; Li Yuan

doi:10.3934/math.20231191

AIMS Mathematics

2023, Volume 8, Issue 10: 23442-23458. doi: 10.3934/math.20231191

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Research article

Further representations and computations of the generalized Moore-Penrose inverse

1.
School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
2.
Department of Mathematics and Computer Science, Hanjiang Normal University, Shiyan, China

Received: 19 May 2023 Revised: 10 July 2023 Accepted: 13 July 2023 Published: 26 July 2023
MSC : 15A09

The aim of this paper is to provide new representations and computations of the generalized Moore-Penrose inverse. Based on the Moore-Penrose inverse, group inverse, Bott-Duffin inverse and certain projections, some representations for the generalized Moore-Penrose inverse are given. An equivalent condition for the continuity of the generalized Moore-Penrose inverse is proposed. Splitting methods and successive matrix squaring algorithm for computing the generalized Moore-Penrose inverse are presented.
- generalized Moore-Penrose inverse,
- representation,
- computation
Citation: Kezheng Zuo, Yang Chen, Li Yuan. Further representations and computations of the generalized Moore-Penrose inverse[J]. AIMS Mathematics, 2023, 8(10): 23442-23458. doi: 10.3934/math.20231191

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Abstract

The aim of this paper is to provide new representations and computations of the generalized Moore-Penrose inverse. Based on the Moore-Penrose inverse, group inverse, Bott-Duffin inverse and certain projections, some representations for the generalized Moore-Penrose inverse are given. An equivalent condition for the continuity of the generalized Moore-Penrose inverse is proposed. Splitting methods and successive matrix squaring algorithm for computing the generalized Moore-Penrose inverse are presented.

References

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