论文信息 - A geometrical approach on generalized inverses by Neumann-type series

A geometrical approach on generalized inverses by Neumann-type series

The convergence of the Neumann-type series to {1,2}-inverses has been shown by K. Tanabe [Linear Algebra Appl. 10 (1975) 163]. In this paper, these results indicating conditions characterizing the convergence of this series to different generalized inverses are extended. In addition, these results for obtaining different generalized inverses from the hyperpower method are applied. Finally, generalized involutory matrices are introduced and characterized using the obtained results.

[1] Adi Ben-Israel,et al. A Hyperpower Iterative Method for Computing Matrix Products Involving the Generalized Inverse , 1971 .

[2] Adi Ben-Israel,et al. Generalized inverses: theory and applications , 1974 .

[3] Robert J. Plemmons,et al. Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[4] K. Tanabe. Neumann-type expansion of reflexive generalized inverses of a matrix and the hyperpower iterative method , 1975 .

[5] W. Petryshyn,et al. On generalized inverses and on the uniform convergence of (I − βK)n with application to iterative methods , 1967 .

[6] Adi Ben-Israel,et al. A note on an iterative method for generalized inversion of matrices , 1966 .

[7] Yimin Wei,et al. A characterization and representation of the generalized inverse A(2)T,S and its applications , 1998 .

[8] R. Hartwig,et al. The hyperpower iteration revisited , 1996 .

[9] Rafael Bru,et al. Group inverse and group involutory Matrices , 1998 .

[10] A. Charnes,et al. Contributions to the Theory of Generalized Inverses , 1963 .