| تعداد نشریات | 32 |
| تعداد شمارهها | 856 |
| تعداد مقالات | 8,310 |
| تعداد مشاهده مقاله | 52,848,833 |
| تعداد دریافت فایل اصل مقاله | 9,274,503 |
Smoothing the absolute value equations by the component-wise analysis | ||
| Journal of Mathematical Modeling | ||
| مقاله 2، دوره 13، شماره 2، مرداد 2025، صفحه 251-262 اصل مقاله (175.65 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.28343.2501 | ||
| نویسنده | ||
| Mandana Moccari* | ||
| Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran | ||
| چکیده | ||
| In this study, an efficient smooth function is introduced to determine the solutions of Absolute Value Equations (AVEs) using a two-step extension of Traub's method. Additionally, a novel approach is proposed for solving AVEs in a component-wise manner. Cubic convergence is achieved under mild assumptions. The results demonstrate that the proposed method is highly effective, as validated by numerical examples. | ||
| کلیدواژهها | ||
| Absolute value equation؛ Traub's method؛ high order of convergence؛ smooth functions | ||
| مراجع | ||
|
[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. | ||
|
آمار تعداد مشاهده مقاله: 256 تعداد دریافت فایل اصل مقاله: 379 |
||