Methods of Gauss–Jordan elimination to compute core inverse and dual core inverse. Issue 12 (13th August 2022)

• Record Type: Journal Article
• Authors: Sheng, Xingping; Xin, Dawei
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 12(2022)
• Page Start: 2354
• Page End: 2366
• Publication Date: 2022-08-13
• Subjects: Core inverse -- dual core inverse -- Gauss–Jordan elimination -- partitioned matrix -- computation complexity; 15A09 -- 65F05; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1796906
• Languages: English
• ISSNs: 0308-1087

Abstract

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 ◯ # and dual core inverse A ◯ # 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.