A new Type of Matrix Splitting and its Applications

A possible type of the matrix splitting is introduced. Using this matrix splitting, we introduce a few properties and representations of generalized inverses as well as iterative methods for computing various solutions of singu- lar linear systems. This matrix splitting is a generalization of the known index splitting from [13] and a proper splitting from [4]. Using a generalization of the condition number and introduced representations of generalized inverses, we ob- tain several norm estimates.

[1]  Yimin Wei.  Index splitting for the Drazin inverse and the singular linear system , 1998, Appl. Math. Comput..

[2]  Z. I. Wozniki,et al.  NONNEGATIVE SPLITTING THEORY , 1994 .

[3]  Zbigniew I. Woźnicki.  Matrix splitting principles , 2001 .

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

[5]  Yong-Lin Chen.  Finite algorithms for the (2)-generalized inverse , 1995 .

[6]  Randall E. Cline,et al.  Inverses of Rank Invariant Powers of a Matrix , 1968 .

[7]  M. Kreĭn,et al.  Linear operators leaving invariant a cone in a Banach space , 1950 .

[8]  P. Robert,et al.  On the group-inverse of a linear transformation , 1968 .

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

[10]  Adi Ben-Israel,et al.  On Error Bounds for Generalized Inverses , 1966 .

[11]  A. Berman,et al.  Cones and Iterative Methods for Best Least Squares Solutions of Linear Systems , 1974 .

[12]  王国荣,et al.  THE PERTURBATION THEORY FOR THE DRAZIN INVERSE AND ITS APPLICATIONS , 1996 .

[13]  Z. Woźnicki,et al.  Nonnegative splitting theory , 1994 .

[14]  A. Berman,et al.  Proper Splittings of Rectangular Matrices , 1976 .

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

[16]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[17]  Stephen Demko,et al.  Condition numbers of rectangular systems and bounds for generalized inverses , 1986 .

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