References
- Ben-Israel A, Greville TNE. Generalized inverses: theory and applications. 2nd ed. New York (NY): Springer; 2003.
- Eiermann M, Marek I, Niethammer W. On the solution of singular linear systems of algebraic equations by semi-iterative methods. Numer Math. 1988;53:265–283. doi: 10.1007/BF01404464
- Hanke M. Iterative consistency: a concept for the solution of singular linear system. SIAM J Matrix Anal Appl. 1994;15:569–577. doi: 10.1137/S0895479890182545
- Hartwig RE, Levine J. Applications of the Drazin inverse to the hill cryptographic system: part III. Cryptologia. 1981;5:67–77. doi: 10.1080/0161-118191855850
- Kirkland SJ, Neumann M, Xu J. Convexity and elasticity of the growth rate in size-classified population models. SIAM J Matrix Anal Appl. 2004;26:170–185. doi: 10.1137/S0895479802411031
- Li X, Wei Y. An improvement on perturbation bounds for the Drazin inverse. Numer Linear Algebra Appl. 2003;10:563–575. doi: 10.1002/nla.325
- Meyer CD. The condition number of a finite Markov chains and perturbation bounds for the limiting probabilities. SIAM J Algebr Discrete Methods. 1980;1:273–283. doi: 10.1137/0601031
- Szyld D. Equivalence of conditions for convergence of iterative methods for singular equations. Numer Linear Algebra Appl. 1994;1:151–154. doi: 10.1002/nla.1680010206
- Wei Y, Li X, Bu F. A perturbation bound of the Drazin inverse of a matrix by separation of simple invariant subspaces. SIAM J Matrix Anal Appl. 2005;27:72–81. doi: 10.1137/S0895479804439948
- Wei Y, Li X, Bu F, Zhang F. Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices – application of perturbation theory for simple invariant subspaces. Linear Algebra Appl. 2006;419:765–771. doi: 10.1016/j.laa.2006.06.015
- Drazin MP. Pseudoinverse in associative rings and semigroups. Amer Math Monthly. 1958;65:506–514. doi: 10.1080/00029890.1958.11991949
- Hartwig RE, Wang G, Wei Y. Some additive results on Drazin inverse. Linear Algebra Appl. 2001;322:207–217. doi: 10.1016/S0024-3795(00)00257-3
- Castro-González N. Additive perturbation results for the Drazin inverse. Linear Algebra Appl. 2005;397:279–297. doi: 10.1016/j.laa.2004.11.001
- Martínez-Serrano MF, Castro-González N. On the Drazin inverse of block matrices and generalized Schur complement. Appl Math Comput. 2009;215:2733–2740.
- Yang H, Liu X. The Drazin inverse of the sum of two matrices and its applications. J Comput Appl Math. 2011;235:1412–1417. doi: 10.1016/j.cam.2010.08.027
- Bu C, Feng C, Bai S. Representations for the Drazin inverses of the sum of two matrices and some block matrices. Appl Math Comput. 2012;218:10226–10237.
- Castro-González N, Dopazo E, Martínez-Serrano MF. On the Drazin inverse of the sum of two operators and its application to operator matrices. J Math Anal Appl. 2008;350:207–215. doi: 10.1016/j.jmaa.2008.09.035
- Wei Y, Deng C. A note on additive results for the Drazin inverse. Linear Multilinear Algebra. 2011;59:1319–1329. doi: 10.1080/03081087.2010.496110
- Chen J, Xu Z, Wei Y. Representations for the Drazin inverse of the sum P+Q+R+S and its applications. Linear Algebra Appl. 2008;430:438–457. doi: 10.1016/j.laa.2008.08.007
- Hartwig RE, Li X, Wei Y. Representations for the Drazin inverse of 2× 2 block matrix. SIAM J Matrix Anal Appl. 2006;27:757–771. doi: 10.1137/040606685
- Hartwig RE, Shoaf JM. Group inverses and Drazin inverses of bidiagonal and triangular Toeplitz matrices. J Austral Math Soc. 1977;24:10–34. doi: 10.1017/S1446788700020036
- Meyer CD, Rose NJ. The index and the Drazin inverse of block triangular matrices. SIAM J Appl Math. 1977;33:1–7. doi: 10.1137/0133001
- Campbell SL, Meyer CD. Generalized inverses of linear transformations. New York (NY): Dover; 1991.
- Mosić D. Expressions for the generalized Drazin inverse of a block matrix in a Banach algebra. Int J Comput Math. 2014;91:514–526. doi: 10.1080/00207160.2013.791684
- Mosić D, Djordjević DS. Representation for the generalized Drazin inverse of block matrices in Banach algebras. Appl Math Comput. 2012;218:12001–12007.
- Mosić D, Djordjević DS. Several expressions for the generalized Drazin inverse of a block matrix in a Banach algebra. Appl Math Comput. 2013;220:374–381.
- Djordjević DS, Stanimirović PS. On the generalized Drazin inverse and generalized resolvent. Czechoslovak Math J. 2001;51:617–634. doi: 10.1023/A:1013792207970
- Mosić D, Zou H, Chen J. The generalized Drazin inverse of the sum in a Banach algebra. Ann Funct Anal. 2017;8:90–105. doi: 10.1215/20088752-3764461
- Miao J. Results of the Drazin inverse of block matrices. J Shanghai Normal Univ. 1989;18:25–31.