Generalized SOR-like iteration method for solving weakly nonlinear systems

References

• M.S. Allen, D. Rixen, M. van der Seijs, P. Tiso, T. Abrahamsson, and R.L. Mayes, Weakly Nonlinear Systems: Modeling and Experimental Methods, Springer International Publishing, New York, 2020.
   Google Scholar
• O. Axelsson, A restarted version of a generalized preconditioned conjugate gradient method, Commun. Appl. Numer. Methods 4 (1988), pp. 521–530.
   Google Scholar
• Z.-Z. Bai, A class of two-stage iterative methods for systems of weakly nonlinear equations, Numer. Algorithms 14 (1997), pp. 295–319.
   Web of Science ®Google Scholar
• Z.-Z. Bai, Modulus-based matrix splitting iteration methods for linear complementarity problems, Numer. Linear Algebra Appl. 17 (2010), pp. 917–933.
   Web of Science ®Google Scholar
• Z.-Z. Bai and X.-P. Guo, On Newton-HSS methods for systems of nonlinear equations with positive-definite Jacobian matrices, J. Comput. Math. 28 (2008), pp. 235–260.
   Web of Science ®Google Scholar
• Z.-Z. Bai and X. Yang, On HSS-based iteration methods for weakly nonlinear systems, Appl. Numer. Math. 59 (2009), pp. 2923–2936.
   Web of Science ®Google Scholar
• Z.-Z. Bai, G.H. Golub, and M.K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl. 24 (2003), pp. 603–626.
   Web of Science ®Google Scholar
• Z.-Z. Bai, B.N. Parlett, and Z.-Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math. 102 (2005), pp. 1–38.
   Web of Science ®Google Scholar
• A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
   Google Scholar
• T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein, Introduction to Algorithms, The MIT Press, Cambridge, 2009.
   Google Scholar
• X. Dong, X.-H. Shao, and H.-L. Shen, A new SOR-like method for solving absolute value equations, Appl. Numer. Math. 156 (2020), pp. 410–421.
   Web of Science ®Google Scholar
• S.A. Edalatpanah, On the preconditioned projective iterative methods for the linear complementarity problems, RAIRO-Oper. Res. 54 (2020), pp. 341–349.
   Web of Science ®Google Scholar
• M. Fallah and S.A. Edalatpanah, On the some new preconditioned generalized AOR methods for solving weighted linear least squares problems, IEEE Access 8 (2020), pp. 33196–33201.
   Web of Science ®Google Scholar
• E.A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, CRC Press, Boca Raton, FL, 2004.
   Google Scholar
• L.-H. Huang, A quasi-Newton algorithm for large-scale nonlinear equations, J. Inequal. Appl. 35 (2017), pp. 1–16.
   Google Scholar
• M.-J. Jiang and X.-P. Guo, A new parameter-free method for Toeplitz systems of weakly nonlinear equations,J. Comput. Appl. Math. 393 (2021), p. 113505.
   Google Scholar
• Y.-F. Ke and C.-F. Ma, On SOR-like iteration methods for solving weakly nonlinear systems, Optim. Methods Softw. (2020), pp. 1–18.
   Web of Science ®Google Scholar
• C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, 1995.
   Google Scholar
• L. Ladislav and V. Jan, New quasi-Newton method for solving systems of nonlinear equations, Appl. Math. 62 (2017), pp. 121–134.
   Web of Science ®Google Scholar
• O.L. Mangasarian and R.R. Meyer, Absolute value equations, Linear Algebra Appl. 419 (2006), pp. 359–367.
   Web of Science ®Google Scholar
• S.-X. Miao, X.-T. Xiong, and J. Wen, On Picard-SHSS iteration method for absolute value equation, AIMS Math. 6 (2021), pp. 1743–1753.
   Web of Science ®Google Scholar
• H.S. Najafi and S.A. Edalatpanah, Iterative methods with analytical preconditioning technique to linear complementarity problems: Application to obstacle problems, RAIRO-Oper. Res. 47 (2013), pp. 59–71.
   Web of Science ®Google Scholar
• H.S. Najafi and S.A. Edalatpanah, Modification of iterative methods for solving linear complementarity problems, Eng. Comput. 30 (2013), pp. 910–923.
   Google Scholar
• H.S. Najafi and S.A. Edalatpanah, On the application of Liao's method for solving linear systems, Ain Shams Eng.J. 4 (2013), pp. 501–505.
   Google Scholar
• H.S. Najafi and S.A. Edalatpanah, A new modified SSOR iteration method for solving augmented linear systems, Int. J. Comput. Math. 91 (2014), pp. 539–552.
   Web of Science ®Google Scholar
• H.S. Najafi and S.A. Edalatpanah, On the modified symmetric successive over-relaxation method for augmented systems, Comput. Appl. Math. 34 (2015), pp. 607–617.
   Google Scholar
• H.S. Najafi, S.A. Edalatpanah, and G.A. Gravvanis, An efficient method for computing the inverse of arrowhead matrices, Appl. Math. Lett. 33 (2014), pp. 1–5.
   Web of Science ®Google Scholar
• H.S. Najafi, S.A. Edalatpanah, and A.H. Sheikhani, Convergence analysis of modified iterative methods to solve linear systems, Mediterr. J. Math. 11 (2014), pp. 1019–1032.
   Web of Science ®Google Scholar
• J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
   Google Scholar
• F. Rahpeymaii, An efficient conjugate gradient trust-region approach for systems of nonlinear equation, Afrika Mat. 30 (2019), pp. 597–609.
   Web of Science ®Google Scholar
• T.S. Siahkolaei and D.K. Salkuyeh, TTSCSP-based iteration methods for complex weakly nonlinear systems, East Asian J. Appl. Math. 10 (2020), pp. 1–21.
   Web of Science ®Google Scholar
• M.Y. Waziri and K. Ahmed J. Sabi'u, A Dai–Liao conjugate gradient method via modified secant equation for system of nonlinear equations, Arab. J. Math. 9 (2020), pp. 443–457.
   Web of Science ®Google Scholar
• T. Wong and M.J. Ward, Weakly nonlinear analysis of peanut-shaped deformations for localized spots of singularly perturbed reaction-diffusion systems, SIAM J. Appl. Dyn. Syst. 19 (2020), pp. 2030–2058.
   Web of Science ®Google Scholar
• H-T Wu, X. Qi, and X.-Y. Xiao, On GSOR-based iteration methods for solving weakly nonlinear systems with complex symmetric coefficient matrices, J. Appl. Math. Comput. 102 (2021), pp. 1–38.
   Google Scholar
• D.M. Young, Iterative Solution of Large Linear Systems, Elsevier, Amsterdam, 2014.
   Google Scholar