[1] Axelsson, O., Kucherov, A.: Real valued iterative methods for solving complex symmetric linear systems. Numer. Linear Algebra Appl. 7, 197-218 (2000)
[2] Bai, Z.-Z.: Block preconditioners for elliptic PDE-constrained optimization problems. Computing 91, 379-395 (2011)
[3] Bai, Z.-Z., Benzi, M., Chen, F.: Modified HSS iteration methods for a class of complex symmetric linear systems. Computing 87, 93-111 (2010)
[4] Bai, Z.-Z., Benzi, M., Chen, F.: On preconditioned MHSS iteration methods for complex symmetric linear systems. Numer. Algorithms 56, 297-317 (2011)
[5] Bai, Z.-Z., Benzi, M., Chen, F., Wang, Z.-Q.: Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems. IMA J. Numer. Anal. 33, 343-369 (2013)
[6] Bai, Z.-Z., Golub, G.H.: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. IMA J. Numer. Anal. 27, 1-23 (2007)
[7] Bai, Z.-Z., Golub, G.H., Li, C.-K.: Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. SIAM J. Sci. Comput. 28, 584-603 (2006)
[8] Bai, Z.-Z., Golub, G.H., Lu, L.-Z., Yin, J.-F.: Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. SIAM J. Sci. Comput. 26, 844-863 (2005)
[9] Bai, Z.-Z., Golub, G.H., Ng, M.K.: Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. SIAM J. Matrix Anal. Appl. 24, 603-626 (2003)
[10] Bai, Z.-Z., Golub, G.H., Ng, M.K.: On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Numer. Linear Algebra Appl. 14, 319-335 (2007)
[11] Bai, Z.-Z., Golub, G.H., Pan, J.-Y.: Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems. Numerische Mathematik 98, 1-32 (2004)
[12] Bai, Z.-Z., Guo, X.-P.: On Newton-HSS methods for systems of nonlinear equations with positive-definite Jacobian matrices. J. Comput. Math. 28, 235-260 (2010)
[13] Bai, Z.-Z., Parlett, B.N., Wang, Z.-Q.: On generalized successive overrelaxation methods for augmented linear systems. Numerische Mathematik 102, 1-38 (2005)
[14] Bai, Z.-Z., Wang, Z.-Q.: On parameterized inexact Uzawa methods for generalized saddle point problems. Linear Algebra Appl. 428, 2900-2932 (2008)
[15] Bai, Z.-Z., Yang, X.: On HSS-based iteration methods for weakly nonlinear systems. Appl. Numer. Math. 59, 2923-2936 (2009)
[16] Benzi, M., Golub, G.H.: A preconditioner for generalized saddle point problems. SIAM J. Matrix Anal. Appl. 26, 20-41 (2004)
[17] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1-137 (2005)
[18] Chen, M.-H., Wu, Q.-B.: On modified Newton-DGPMHSS method for solving nonlinear systems with complex symmetric Jacobian matrices. Comput. Math. Appl. 76, 45-57 (2018)
[19] da Cunha, R.D., Becker, D.: Dynamic block GMRES: an iterative method for block linear systems. Adv. Comput. Math. 27, 423-448 (2007)
[20] Darvishi, M.T., Barati, A.: A third-order Newton-type method to solve systems of nonlinear equations. Appl. Math. Comput. 187, 630-635 (2007)
[21] Dembo, R., Eisenstat, S., Steihaug, T.: Inexact Newton method. SIAM J. Numer. Anal. 19, 400-408 (1982)
[22] Deuflhard, P.: Newton Methods for Nonlinear Problems. Springer-Verlag, Berlin, Heidelberg (2004)
[23] Edalatpour, V., Hezari, D., Salkuyeh, D.K.: Accelerated generalized SOR method for a class of complex systems of linear equations. Math. Commun. 20, 37-52 (2015)
[24] Elman, H.C.: Preconditioners for saddle point problems arising in computational fluid dynamics. Appl. Numer. Math. 43, 75-89 (2002)
[25] Elman, H.C., Silvester, D.J., Wathen, A.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics. Oxford University Press, Oxford (2014)
[26] Feng, Y.-Y., Wu, Q.-B.: MN-PGSOR method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices. J. Math. 2021, 1-18 (2021)
[27] Feriani, A., Perotti, F., Simoncini, V.: Iterative system solvers for the frequency analysis of linear mechanical systems. Comp. Methods Appl. Mech. Eng. 190, 1719-1739 (2000)
[28] Guo, X.-P., Duff, I.S.: Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations. Numer. Linear Algebra Appl. 18, 299-315 (2011)
[29] Hezari, D., Edalatpour, V., Salkuyeh, D.K.: Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations. Numer. Linear Algebra Appl. 22, 761-776 (2015)
[30] Huang, Z.-G., Wang, L.-G., Xu, Z., Cui, J.-J.: Preconditioned accelerated generalized successive overrelaxation method for solving complex symmetric linear systems. Comput. Math. Appl. 77, 1902-1916 (2019)
[31] Karlsson, H.O.: The quasi-minimal residual algorithm applied to complex symmetric linear systems in quantum reactive scattering. J. Chem. Phys. 103, 4914-4919 (1995)
[32] Kuramoto, Y.: Oscillations Chemical Waves and Turbulence. Dover, Mineola (2003)
[33] Li, C.-X., Wu, S.-L.: A double-parameter GPMHSS method for a class of complex symmetric linear systems from Helmholtz equation. Math. Prob. Eng. 2014, 1-7 (2014)
[34] Li, Y., Guo, X.-P.: Semilocal convergence analysis for MMN-HSS methods under the Hölder conditions. East Asia J. Appl. Math. 7, 396-416 (2017)
[35] Li, Y., Guo, X.-P.: Multi-step modified Newton-HSS methods for systems of nonlinear equations with positive definite Jacobian matrices. Numer. Algorithms 75, 55-80 (2017)
[36] Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Society for Industrial and Applied Mathematics, Philadelphia, PA (2000)
[37] Pan, J.-Y., Ng, M.K., Bai, Z.-Z.: New preconditioners for saddle point problems. Appl. Math. Comput. 172, 762-771 (2006)
[38] Papp, D., Vizvari, B.: Effective solution of linear Diophantine equation systems with an application in chemistry. J. Math. Chem. 39, 15-31 (2006)
[39] Qi, X., Wu, H.-T., Xiao, X.-Y.: Modified Newton-GSOR method for solving complex nonlinear systems with symmetric Jacobian matrices. Comput. Appl. Math. 39, 1-18 (2020)
[40] Qi, X., Wu, H.-T., Xiao, X.-Y.: Modified Newton-AGSOR method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices. Calcolo 57, 1-23 (2020)
[41] Raviart, P.A., Girault, V.: Finite Element Approximation of the Navier-Stokes Equations. Springer Verlag, Berlin, New York (1979)
[42] Rees, T., Dollar, H.S., Wathen, A.J.: Optimal solvers for PDE-constrained optimization. SIAM Journal on Scientific Computing 32, 271-298 (2010)
[43] Rees, T., Stoll, M.: Block-triangular preconditioners for PDE-constrained optimization. Numer. Linear Algebra Appl. 17, 977-996 (2010)
[44] Rheinboldt, W.C.: Methods for Solving Systems of Nonlinear Equations. Society for Industrial and Applied Mathmatics, Philadelphia, PA (1998)
[45] Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia, PA (2003)
[46] Salkuyeh, D.K., Hezari, D., Edalatpour, V.: Generalized successive overrelaxation iterative method for a class of complex symmetric linear system of equations. Int. J. Comp. Math. 92, 802-815 (2015)
[47] Sulem, C., Sulem, P.L.: The Nonlinear Schrödinger Equation Self-focusing and Wave Collapse. Springer, New York (2007)
[48] Wang, J., Guo, X.-P., Zhong, H.-X.: Accelerated GPMHSS method for solving complex systems of linear equations. East Asia J. Appl. Math. 7, 143-155 (2017)
[49] Wang, J., Guo, X.-P., Zhong, H.-X.: DPMHSS iterative method for systems of nonlinear equations with block two-by-two complex Jacobian matrices. Numer. Algorithms 77, 167-184 (2018)
[50] Wu, Q.-B., Chen, M.-H.: Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations. Numer. Algorithms 64, 659-683 (2013)
[51] Xiao, X.-Y., Wang, X., Yin, H.-W.: Efficient single-step preconditioned HSS iteration methods for complex symmetric linear systems. Comput. Math. Appl. 74, 2269-2280 (2017)
[52] Xie, F., Lin, R.-F., Wu, Q.-B.: Modified Newton-DSS method for solving a class of systems of nonlinear equations with complex symmetric Jacobian matrices. Numer. Algorithms 85, 951-975 (2020)
[53] Yang, A.-L., Wu, Y.-J.: Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices. Numer. Algebra Control Optim. 2, 839-853 (2012)
[54] Zhong, H.-X., Chen, G.-L., Guo, X.-P.: On preconditioned modified Newton-MHSS method for systems of nonlinear equations with complex symmetric Jacobian matrices. Numer. Algorithms 69, 553-567 (2015)
[55] Zhu, M.-Z., Zhang, G.-F.: A class of iteration methods based on HSS for Topelitz systems of weakly nonlinear equations. Journal of Computational and Applied Mathematics 290, 433-444 (2015)
