New sufficient conditions for the solvability of a new class of Sylvester-like absolute value matrix equation

Shubham Kumar; Deepmala; Roshan Lal  Keshtwal

doi:10.33993/jnaat522-1321

Authors

Shubham Kumar PDPM IIITDM Jabalpur, India https://orcid.org/0000-0001-5237-9719
Deepmala PDPM IIITDM Jabalpur, India
Roshan Lal Keshtwal VSKC Government Postgraduate College Dakpathar, India https://orcid.org/0000-0001-6616-943X

DOI:

https://doi.org/10.33993/jnaat522-1321

Keywords:

New class of Sylvester-like Absolute value matrix equation, Sufficient condition, Unique solution

Abstract views: 146

Abstract

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.

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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