The unique solvability conditions for a new class of absolute value equation

Kumar, Shubham; Deepmala, D

doi:10.2298/yjor220515036k

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…So these results may be also applicable for the NGAVE (6.4) and Ax − |Bx − c| = d to ensure their unique solvability of them, because in both the equations matrices A and B appears. For example conditions σ max (B) < σ min (A) ensure the unique solution of the NGAVE (6.4) for any d [44] and this condition easily can be proved for the unique solution of Ax − |Bx − c| = d. For more about AVE Ax − |Bx − c| = d one may refer [13]. ), these results are studied by many authors in the literature (see [14,15,16,34,40] and references therein).…”

Section: New Generalized Absolute Value Equationmentioning

confidence: 92%

A Note on Unique Solvability of the Generalized Absolute Value Matrix Equation

Kumar

Deepmala

2023

Natl. Acad. Sci. Lett.

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In this survey paper, we focus on the necessary and sufficient conditions for the unique solvability and unsolvability of the absolute value equations (AVEs) during the last twenty years (2004 to 2023). We discussed unique solvability conditions for various types of AVEs like standard absolute value equation (AVE), Generalized AVE (GAVE), New generalized AVE (NGAVE), Triple AVE (TAVE) and a class of NGAVE based on interval matrix, P-matrix, singular value conditions, spectral radius and W-property. Based on unique solution of AVEs, we also discussed unique solvability conditions for linear complementarity problems (LCP) and horizontal linear complementarity problems (HLCP).

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Section: New Generalized Absolute Value Equationmentioning

confidence: 92%

A Note on Unique Solvability of the Generalized Absolute Value Matrix Equation

Kumar

Deepmala

2023

Natl. Acad. Sci. Lett.

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“…[7]). Let all diagonal entry of AC −1 + I have the same sign as the corresponding entries of AC −1 − I.…”

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confidence: 99%

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

Kumar,

Deepmala,

Keshtwal

2023

J. Numer. Anal. Approx. Theory

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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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