Back
 JAMP  Vol.5 No.9 , September 2017
The SMW Formula for Bounded Homogeneous Generalized Inverses with Applications
Abstract: In this paper, we present an extension of the so-called classical Sherman-Morrison-Woodbury (for short SMW) formula for bounded homogeneous generalized inverse in Banach spaces. Some particular cases and applications will be also considered. Our results generalize the results of many authors for finite dimensional matrices and Hilbert space operators in the literature.
Cite this paper: Cao, J. (2017) The SMW Formula for Bounded Homogeneous Generalized Inverses with Applications. Journal of Applied Mathematics and Physics, 5, 1702-1709. doi: 10.4236/jamp.2017.59143.
References

[1]   Ding, J. and Zhou, A.-H. (2008) A Spectrum Theorem for Perturbed Bounded Linear Operators. Applied Mathematics and Computation, 201, 723-728.
https://doi.org/10.1016/j.amc.2008.01.008

[2]   Riedel, K.S. (1992) A Sherman-Morrison-Woodbury Identity for Rank Augmenting Matrices with Application to Centering. SIAM Journal on Matrix Analysis and Applications, 13, 659-662.
https://doi.org/10.1137/0613040

[3]   Deng, Ch. (2011) A Generalization of the Sherman-Morrison-Woodbury Formula. Applied Mathematics Letters, 24, 1561-1564.
https://doi.org/10.1016/j.aml.2011.03.046

[4]   Duan, Y.T. (2013) A Generalization of the SMW Formula of Operator to the 2-Inverse Case. Abstract and Applied Analysis, 2013, Article ID: 694940.

[5]   Ogawa, H. (1988) An Operator Pseudo-inversion Lemma. SIAM Journal on Applied Mathematics, 48, 1527-1531.
https://doi.org/10.1137/0148095

[6]   Nashed, M.Z. and Votruba, G.F. (1976) Generalized Inverses and Applications. Academic Press, New York, 1-109.

[7]   Wang, Y. and Li, S. (2005) Homogeneous Generalized Inverses of Linear Operators in Banach Spaces. Acta Mathematica Sinica, 48, 253-258.

[8]   Bai, X.Y., et al. (2009) Definition and Criterion of Homogeneous Generalized Inverse. Acta Mathematica Sinica, Chinese Series, 52, 353-360.

[9]   Liu, P. and Wang, Y.W. (2007) The Best Generalized Inverse of the Linear Operator in Normed Linear Space. Linear Algebra and Its Applications, 420, 9-19.
https://doi.org/10.1016/j.laa.2006.04.024

[10]   Cao, J.B. and Xue, Y.F. (2014) Perturbation Analysis of Bounded Homogeneous Operator Generalized Inverses in Banach Spaces. Acta Mathematica Universitatis Comenianae, 83, 181-194.

 
 
Top