Methods of Gauss–Jordan elimination to compute core inverse and dual core inverse

Abstract

In this paper, two formulas, which were studied by Wang and Liu (2015) and Ma and Li (2019), respectively, for the core inverse, are simplified. Then two methods for computing the core inverse $A^{◯\mathrm{\#}}$ and dual core inverse $A_{◯\mathrm{\#}}$ are investigated through Gauss–Jordan elimination on the two appropriate block partitioned matrices. The corresponding algorithms are also summarized. The computational complexities of the these two algorithms are analysed in detail. In the end, some numerical examples are presented to demonstrate the efficiency of the two algorithms.

Keywords:

• Core inverse
• dual core inverse
• Gauss–Jordan elimination
• partitioned matrix
• computation complexity

AMS Subject Classifications(2000):

• 15A09
• 65F05

Acknowledgements

The authors wish to express their sincere thanks to the two anonymous referees for their helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project was supported by NSF China (no.11771076), NSF Anhui Province (No. 2008085MA12).