Computation of {2, 4} and {2, 3}-inverses based on rank-one updates. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Stanimirović, Predrag S.; Katsikis, Vasilios N.; Pappas, Dimitrios
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 1(2018)
• Page Start: 147
• Page End: 166
• Publication Date: 2018-01-02
• Subjects: Generalized inverse -- {2 -- 3}-inverses -- {2 -- 4}-inverses -- Moore–Penrose inverse -- rank-one update; 15A09; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1290042
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: Two finite recurrent procedures for computing and -inverses of a matrix are presented. Each of introduced methods exploits certain matrix product which includes the Moore–Penrose inverse of a symmetric matrix and a generalization of the Sherman-Morrison formula to the case of the Moore–Penrose inverse of a symmetrically rank one modified matrix. The computational complexity of the methods is analysed. In the essence, presented representations investigate dual methods with respect to these introduced in [Stanimirović PS, Katsikis VN, Pappas D, Computing {2, 4} and {2, 3}-inverses by using the Sherman-Morrison formula, Appl. Math. Comput. 2016;273:584–603].