A characterization and representation of the generalized inverse A(2)T,S and its applications

Abstract This paper presents an explicit expression for the generalized inverse A (2) T , S . Based on this, we established the characterization, the representation theorem and the limiting process for A (2) T , S . As an application, we estimate the error bound of the iterative method for approximating A (2) T , S .

[1]  Chen Yonglin,et al.  The generalized Bott-Duffin inverse and its applications , 1990 .

[2]  C. D. Meyer,et al.  Generalized inverses of linear transformations , 1979 .

[3]  M. Nashed Inner, outer, and generalized inverses in banach and hilbert spaces , 1987 .

[4]  G. Styan,et al.  Equalities and Inequalities for Ranks of Matrices , 1974 .

[5]  K. S. Banerjee Generalized Inverse of Matrices and Its Applications , 1973 .

[6]  Adi Ben-Israel On Matrices of Index Zero or One , 1969 .

[7]  Wei Yimin,et al.  The perturbation theory for the Drazin inverse and its applications , 1997 .

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

[9]  Francis Hsuan,et al.  2 - Inverses and Their Statistical Application , 1988 .

[10]  Charles W. Groetsch,et al.  Representations of the generalized inverse , 1975 .

[11]  Francis Hsuan,et al.  The {2}-inverse with applications in statistics , 1985 .

[12]  Mårten Gulliksson Iterative refinement for constrained and weighted linear least squares , 1994 .

[13]  T. Markham,et al.  A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse , 1974 .

[14]  Martin Hanke,et al.  Preconditionings and splittings for rectangular systems , 1990 .

[15]  R. Duffin,et al.  On the algebra of networks , 1953 .

[16]  Wei Yimin,et al.  A Characterization and Representation of the Drazin Inverse , 1996 .

[17]  Musheng Wei,et al.  Structures and uniqueness conditions of MK-weighted pseudoinverses , 1994 .

[18]  L. Eldén A weighted pseudoinverse, generalized singular values, and constrained least squares problems , 1982 .

[19]  M. Z. Nashed,et al.  Convergence of Newton-like methods for singular operator equations using outer inverses , 1993 .

[20]  Randall E. Cline,et al.  A Drazin inverse for rectangular matrices , 1980 .

[21]  Sujit Kumar Mitra,et al.  Partial orders based on outer inverses , 1992 .

[22]  Miroslav Fiedler,et al.  A characterization of the Moore-Penrose inverse , 1993 .