New sufficient conditions for the solvability of a new class of Sylvester-like absolute value matrix equation
DOI:
https://doi.org/10.33993/jnaat522-1321Keywords:
New class of Sylvester-like Absolute value matrix equation, Sufficient condition, Unique solutionAbstract
In this article, some new sufficient conditions for the unique solvability of a new class of Sylvester-like absolute value matrix equation \(AXB - \vert CXD \vert =F\) are given. This work is distinct from the published work by Li [Journal of Optimization Theory and Application, 195(2), 2022]. Some new conditions were also obtained, which were not covered by Li. We also provided an example in support of our result.
Downloads
References
R.W. Cootle, J.S. Pang, R.E. Stone, The linear complementarity problem, Acad. Press, New York, 1992.
M. Dehghan, A. Shirilord, Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation, Appl. Numer. Math., 158 (2020), pp.425–438. https://doi.org/10.1016/j.apnum.2020.08.001. DOI: https://doi.org/10.1016/j.apnum.2020.08.001
B. Hashemi, Sufficient conditions for the solvability of a Sylvester-like absolute value matrix equation, Appl. Math. Lett., 112 (2021), p. 106818, https://doi.org/10.1016/j.aml.2020.106818. DOI: https://doi.org/10.1016/j.aml.2020.106818
R.A. Horn, C.R. Johnson, Topics in matrix analysis, Cambridge university press, 1994.
S. Kumar, Deepmala, A note on the unique solvability condition for generalized absolute value matrix equation, J. of Numer. Anal. Approx. Theory, 51 (2022) no. 1,pp. 83-87. https://doi.org/10.33993/jnaat511-1263. DOI: https://doi.org/10.33993/jnaat511-1263
S. Kumar, Deepmala A note on unique solvability of the generalized absolute value matrix equation, Natl. Acad. Sci. Lett., 46 (2023) no. 2, pp. 129-131. https://doi.org/10.1007/s40009-022-01193-9. DOI: https://doi.org/10.1007/s40009-022-01193-9
S. Kumar, Deepmala, The unique solvability conditions for a new class of absolute value equation, Yugosl. J. Oper. Res., 33 (2022) no. 3, pp. 425-434. http://dx.doi.org/10.2298/YJOR220515036K. DOI: https://doi.org/10.2298/YJOR220515036K
C.X. Li, Sufficient conditions for the unique solution of a new class of Sylvester-like absolute value equations, J. Optim. Theory Appl., 195 (2022) no. 2, pp. 676-683. https://doi.org/10.1007/s10957-022-02106-y. DOI: https://doi.org/10.1007/s10957-022-02106-y
O.L. Mangasarian, R.R. Meyer, Absolute value equations, Linear Algebra Appl., 419 (2006) pp. 359–367. https://doi.org/10.1016/j.laa.2006.05.004. DOI: https://doi.org/10.1016/j.laa.2006.05.004
K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming, Internet edition, 1997.
J. Rohn, A theorem of the alternatives for the equation Ax +B|x| = b, Linear Multilinear Algebra, 52(2004) no. 6, pp. 421-426. https://doi.org/10.1080/0308108042000220686. DOI: https://doi.org/10.1080/0308108042000220686
J. Rohn, Forty necessary and sufficient conditions for regularity of interval matrices: A survey, Electron. J. Linear Algebra, 18 (2009), pp. 500-512. https://doi.org/10.13001/1081-3810.1327. DOI: https://doi.org/10.13001/1081-3810.1327
A. Neumaier, Interval methods for systems of equations, Cambridge university press, 1990. DOI: https://doi.org/10.1017/CBO9780511526473
N.P. Seif, S.A. Hussein, A.S. Deif, The interval Sylvester equation, Computing, 52 (1994) no. 3, pp. 233-244. https://doi.org/10.1007/BF02246505. DOI: https://doi.org/10.1007/BF02246505
V.N. Shashikhin, Robust assignment of poles in large-scale interval systems, Autom. Remote. Control., 63 (2002), pp. 200-208. https://doi.org/10.1023/A:1014239423012. DOI: https://doi.org/10.1023/A:1014239423012
R. Sznajder, M.S. Gowda, Generalizations of P0- and P-properties; Extended vertical and horizontal linear complementarity problems, Linear Algebra Appl., 223 (1995), pp. 695–715. https://doi.org/10.1016/0024-3795(93)00184-2. DOI: https://doi.org/10.1016/0024-3795(93)00184-2
W.L. Tang, S.X. Miao, On the solvability and Picard-type method for absolute value matrix equations, Comput. Appl. Math., 41 (2022) no. 2, p. 78. https://doi.org/10.1007/s40314-022-01782-w. DOI: https://doi.org/10.1007/s40314-022-01782-w
L.M. Wang, C.X. Li, New sufficient conditions for the unique solution of a square Sylvester-like absolute value equation, Appl. Math. Lett., 116 (2021), p. 106966. https://doi.org/10.1016/j.aml.2020.106966. DOI: https://doi.org/10.1016/j.aml.2020.106966
S.L. Wu, The unique solution of a class of the new generalized absolute value equation, Appl. Math. Lett., 116 (2021), p. 107029. https://doi.org/10.1016/j.aml.2021.107029. DOI: https://doi.org/10.1016/j.aml.2021.107029
K. Xie, On the unique solvability of the generalized absolute value matrix equation, Am. J. Appl. Math., 9(2021) no. 4, p. 104. https://doi.org/10.11648/j.ajam.20210904.12 DOI: https://doi.org/10.11648/j.ajam.20210904.12
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Shubham Kumar, Deepmala, Roshan Lal Keshtwal
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Funding data
-
Ministry of Education, India
Grant numbers MA19S43033021