-
Previous Article
Output regulation for discrete-time nonlinear stochastic optimal control problems with model-reality differences
- NACO Home
- This Issue
-
Next Article
A gradient algorithm for optimal control problems with model-reality differences
Matrix group monotonicity using a dominance notion
1. | Department of Mathematics, National Institute of Technology Raipur, Raipur- 492010, India |
References:
[1] |
A. Ben-Israel and T. N. E. Greville, Generalized Inverses. Theory and Applications, Springer-Verlag, New York, 2003. |
[2] |
A. Berman and R. J. Plemmons, Cones and iterative methods for best square least squares solutions of linear systems, SIAM J. Numer. Anal., 11 (1974), 145-154. |
[3] |
A. Berman and R. J. Plemmons, Monotonicity and the generalized inverse, SIAM J. Appl. Math., 22 (1972), 155-161. |
[4] |
A. Berman and R. J. Plemmons, Matrix group monotonicity, Proceedings of the American Mathematical Society, 46 (1974), 355-359. |
[5] |
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994.
doi: 10.1137/1.9781611971262. |
[6] |
G. Chen and X. Chen, A new splitting for singular linear system and Drazin inverse, J. East China Norm. Univ. Natur. sci. Ed., 3 (1996), 12-18. |
[7] |
L. Collatz, Functional Analysis and Numerical Mathematics, Academic, New York, 1966. |
[8] |
L. Jena and D. Mishra, BD-splittings of matrices, Linear Algebra and Applications, 437 (2012), 1162-1173.
doi: 10.1016/j.laa.2012.04.009. |
[9] |
O. L. Mangasarian, Characterization of real matrices of monotone kind, SIAM Review, 10 (1968), 439-441. |
[10] |
D. Mishra and K. C. Sivakumar, A dominance notion of singular matrices with applications to nonnegative generalized inverses, Linear and Multilinear Algebra, 60 (2012), 911-920.
doi: 10.1080/03081087.2011.632378. |
[11] |
W. C. Pye, Nonnegative Drazin inverses, Linear Algebra Appl., 30 (1980), 149-153.
doi: 10.1016/0024-3795(80)90190-1. |
[12] |
F. Szidarovszky and K. Okuguchi, A general scheme for matrices with nonnegative inverse, PU.M.A. Ser. B, 1 (1990), 109-114. |
[13] |
R. S. Varga, Matrix Iterative Analysis, Springer-Verlag, Berlin, 2000.
doi: 10.1007/978-3-642-05156-2. |
[14] |
Y. Wei, Index splitting for the Drazin inverse and the singular linear system, Appl. Math. Comput., 95 (1998), 115-124.
doi: 10.1016/S0096-3003(97)10098-4. |
[15] |
Y. Wei and H. Wu, Additional results on index splittings for Drazin inverse solutions of singular linear systems, Electron. J. Linear Algebra, 85 (2001), 83-93. |
[16] |
Y. Wei and H. Wu, Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index, Journal of Computational and Applied Mathematics, 114 (2000), 305-318.
doi: 10.1016/S0377-0427(99)90237-6. |
show all references
References:
[1] |
A. Ben-Israel and T. N. E. Greville, Generalized Inverses. Theory and Applications, Springer-Verlag, New York, 2003. |
[2] |
A. Berman and R. J. Plemmons, Cones and iterative methods for best square least squares solutions of linear systems, SIAM J. Numer. Anal., 11 (1974), 145-154. |
[3] |
A. Berman and R. J. Plemmons, Monotonicity and the generalized inverse, SIAM J. Appl. Math., 22 (1972), 155-161. |
[4] |
A. Berman and R. J. Plemmons, Matrix group monotonicity, Proceedings of the American Mathematical Society, 46 (1974), 355-359. |
[5] |
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994.
doi: 10.1137/1.9781611971262. |
[6] |
G. Chen and X. Chen, A new splitting for singular linear system and Drazin inverse, J. East China Norm. Univ. Natur. sci. Ed., 3 (1996), 12-18. |
[7] |
L. Collatz, Functional Analysis and Numerical Mathematics, Academic, New York, 1966. |
[8] |
L. Jena and D. Mishra, BD-splittings of matrices, Linear Algebra and Applications, 437 (2012), 1162-1173.
doi: 10.1016/j.laa.2012.04.009. |
[9] |
O. L. Mangasarian, Characterization of real matrices of monotone kind, SIAM Review, 10 (1968), 439-441. |
[10] |
D. Mishra and K. C. Sivakumar, A dominance notion of singular matrices with applications to nonnegative generalized inverses, Linear and Multilinear Algebra, 60 (2012), 911-920.
doi: 10.1080/03081087.2011.632378. |
[11] |
W. C. Pye, Nonnegative Drazin inverses, Linear Algebra Appl., 30 (1980), 149-153.
doi: 10.1016/0024-3795(80)90190-1. |
[12] |
F. Szidarovszky and K. Okuguchi, A general scheme for matrices with nonnegative inverse, PU.M.A. Ser. B, 1 (1990), 109-114. |
[13] |
R. S. Varga, Matrix Iterative Analysis, Springer-Verlag, Berlin, 2000.
doi: 10.1007/978-3-642-05156-2. |
[14] |
Y. Wei, Index splitting for the Drazin inverse and the singular linear system, Appl. Math. Comput., 95 (1998), 115-124.
doi: 10.1016/S0096-3003(97)10098-4. |
[15] |
Y. Wei and H. Wu, Additional results on index splittings for Drazin inverse solutions of singular linear systems, Electron. J. Linear Algebra, 85 (2001), 83-93. |
[16] |
Y. Wei and H. Wu, Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index, Journal of Computational and Applied Mathematics, 114 (2000), 305-318.
doi: 10.1016/S0377-0427(99)90237-6. |
[1] |
Chinmay Kumar Giri. Index-proper nonnegative splittings of matrices. Numerical Algebra, Control and Optimization, 2016, 6 (2) : 103-113. doi: 10.3934/naco.2016002 |
[2] |
Litismita Jena, Sabyasachi Pani. Index-range monotonicity and index-proper splittings of matrices. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 379-388. doi: 10.3934/naco.2013.3.379 |
[3] |
Haifeng Ma, Xiaoshuang Gao. Further results on the perturbation estimations for the Drazin inverse. Numerical Algebra, Control and Optimization, 2018, 8 (4) : 493-503. doi: 10.3934/naco.2018031 |
[4] |
Kien Trung Nguyen, Vo Nguyen Minh Hieu, Van Huy Pham. Inverse group 1-median problem on trees. Journal of Industrial and Management Optimization, 2021, 17 (1) : 221-232. doi: 10.3934/jimo.2019108 |
[5] |
Meixin Xiong, Liuhong Chen, Ju Ming, Jaemin Shin. Accelerating the Bayesian inference of inverse problems by using data-driven compressive sensing method based on proper orthogonal decomposition. Electronic Research Archive, 2021, 29 (5) : 3383-3403. doi: 10.3934/era.2021044 |
[6] |
Michael Herty, Giuseppe Visconti. Kinetic methods for inverse problems. Kinetic and Related Models, 2019, 12 (5) : 1109-1130. doi: 10.3934/krm.2019042 |
[7] |
Guanghui Hu, Peijun Li, Xiaodong Liu, Yue Zhao. Inverse source problems in electrodynamics. Inverse Problems and Imaging, 2018, 12 (6) : 1411-1428. doi: 10.3934/ipi.2018059 |
[8] |
S. Yu. Pilyugin. Inverse shadowing by continuous methods. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 29-38. doi: 10.3934/dcds.2002.8.29 |
[9] |
Colin Guillarmou, Antônio Sá Barreto. Inverse problems for Einstein manifolds. Inverse Problems and Imaging, 2009, 3 (1) : 1-15. doi: 10.3934/ipi.2009.3.1 |
[10] |
Sergei Avdonin, Pavel Kurasov. Inverse problems for quantum trees. Inverse Problems and Imaging, 2008, 2 (1) : 1-21. doi: 10.3934/ipi.2008.2.1 |
[11] |
Maciej Zworski. A remark on inverse problems for resonances. Inverse Problems and Imaging, 2007, 1 (1) : 225-227. doi: 10.3934/ipi.2007.1.225 |
[12] |
Victor Isakov, Joseph Myers. On the inverse doping profile problem. Inverse Problems and Imaging, 2012, 6 (3) : 465-486. doi: 10.3934/ipi.2012.6.465 |
[13] |
Fabrizio Colombo, Irene Sabadini, Frank Sommen. The inverse Fueter mapping theorem. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1165-1181. doi: 10.3934/cpaa.2011.10.1165 |
[14] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems and Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[15] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems and Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[16] |
Leonardo Marazzi. Inverse scattering on conformally compact manifolds. Inverse Problems and Imaging, 2009, 3 (3) : 537-550. doi: 10.3934/ipi.2009.3.537 |
[17] |
Siamak RabieniaHaratbar. Inverse scattering and stability for the biharmonic operator. Inverse Problems and Imaging, 2021, 15 (2) : 271-283. doi: 10.3934/ipi.2020064 |
[18] |
Guillaume Bal, Alexandre Jollivet. Stability estimates in stationary inverse transport. Inverse Problems and Imaging, 2008, 2 (4) : 427-454. doi: 10.3934/ipi.2008.2.427 |
[19] |
Janne M.J. Huttunen, J. P. Kaipio. Approximation errors in nonstationary inverse problems. Inverse Problems and Imaging, 2007, 1 (1) : 77-93. doi: 10.3934/ipi.2007.1.77 |
[20] |
Henk Bruin, Sonja Štimac. On isotopy and unimodal inverse limit spaces. Discrete and Continuous Dynamical Systems, 2012, 32 (4) : 1245-1253. doi: 10.3934/dcds.2012.32.1245 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]