[1] J.H. Alcantara, J.S. Chen, M.K. Tam, Method of alternating projections for the general absolute
value equation, J. Fixed Point Theory Appl. 25 (2023) 39.
[2] F.H. Clarke, Optimization and Nonsmooth Analysis, SIAM, 1990.
[3] V. Edalatpour, D. Hezari, D.K. Salkuyeh, A generalization of the gauss–seidel iteration method for
solving absolute value equations, Appl. Math. Comput. 293 (2017) 156–167.
[4] R. Farhadsefat, T. Lotfi, J. Rohn, A note on regularity and positive definiteness of interval matrices,
Open Math. 10 (2012) 322–328.
[5] J. Feng, S. Liu, An improved generalized Newton method for absolute value equations, SpringerPlus
5 (2016) 1042.
[6] J. Feng, S. Liu, A new two-step iterative method for solving absolute value equations, Inequal.
Appl. 2019 (2019) 39.
[7] M. Grau-Sanchez, M. Noguera, J. Gutierrez, On some computational orders of convergence, Appl.
Math. Lett. 23 (2010) 472–478.
[8] F.K. Haghani, On generalized Traubs method for absolute value equations, J. Optim. Theory Appl.
166 (2015) 619–625.
[9] F. Hashemi, S. Ketabchi, Numerical comparisons of smoothing functions for optimal correction of
an infeasible system of absolute value equations, Numer. Algebra Control Optim. 10 (2019) 13–21.
[10] N.J. Higham, Functions of Matrices: Theory and Computation, SIAM, 2008.
[11] S.L. Hu, Z.H. Huang, Q. Zhang, A generalized Newton method for absolute value equations asso-
ciated with second order cones, J. Comput. Appl. Math. 235 (2011) 1490–1501.
[12] X. Jiang, Y. Zhan, A smoothing-type algorithm for absolute value equations., J. Ind. Manag. Optim.
9 (2013) 4.
[13] E. Khosravi Dehdezi, S. Karimi, A fast and efficient newton-shultz-type iterative method for com-
puting inverse and moore-penrose inverse of tensors, J. Math. Model. 9 (2021) 645–664.
[14] T. Lotfi, H. Vieseh, A note on unique solvability of the absolute value equation, J. Linear. Topolog-
ical Algebra. 2 (2013) 77–81.
[15] W.H. Luo, J. Guo, L. Yin, A dimension expanded newton-type method for absolute value equations,
J. Appl. Math. Comput. 70 (2024) 3219–3233.
[16] O. Mangasarian, A generalized Newton method for absolute value equations, Optim. Lett.3 (2009)
101–108.
[17] O. Mangasarian, R. Meyer, Absolute value equations, Linear Algebra Appl. 419 (2006) 359–367.
[18] M. Moccari, T. Lotfi, V. Torkashvand, On the stability of a two-step method for a fourth-degree
family by computer designs along with applications, Int. J. Nonlinear Anal. Appl. 14 (2023) 261–
282.
[19] P.M. Pardalos, The linear complementarity problem in: Advances in Optimization and Numerical
Analysis, Springer, 1994.
[20] L. Qi, J. Sun, A nonsmooth version of Newton’s method, Math. Program. 58 (1993) 353–367.
[21] J. Rohn, A theorem of the alternatives for the equation Ax + B|x| = b, Linear Multilinear A. 52
(2004) 421-426.
[22] J. Tang, J. Zhou, A quadratically convergent descent method for the absolute value equation Ax +
B|x| = b, Oper. Res. Lett. 47 (2019) 229–234.
[23] H. Wozniakowski, Numerical stability for solving nonlinear equations, Numer. Math. 27 (1976)
373–390.
[24] N. Yilmaz, Introducing three new smoothing functions: Analysis on smoothing-newton algorithms,
J. Math. Model. 463-479 (2024) 463–479.
[25] N. Yilmaz, A. Sahiner, Smoothing techniques in solving non-lipschitz absolute value equations, Int.
J. Comput. Math. 100 (2023) 867–879.
[26] N. Zainali, T. Lotfi, On developing a stable and quadratic convergent method for solving absolute
value equation, J. Comput. Appl. Math. 330 (2018) 742–747.
[27] C. Zhang, Q. Wei, Global and finite convergence of a generalized Newton method for absolute
value equations, Optim. Theory Appl. 143 (2009) 391–403.
[28] R. Ziadi, A. Bencherif-Madani, A mixed algorithm for smooth global optimization, J. Math. Model.
11 (2023) 207–228.
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