[1] Bai, Z.J., Bai, Z.Z.: On nonsingularity of block two-by-two matrices. Linear Algebra Appl. 439(8), 2388-2404 (2013)
[2] Bai, Z.Z.: Structured preconditioners for nonsingular matrices of block two-by-two structures. Math. Comput. 75(254), 791-815 (2006)
[3] Bai, Z.Z.: Optimal parameters in the HSS-like methods for saddle-point problems. Numer. Linear Algebra Appl. 16(6), 447-479 (2009)
[4] Bai, Z.Z.: Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks. J. Comput. Appl. Math. 237(1), 295-306 (2013)
[5] Bai, Z.Z.: On preconditioned iteration methods for complex linear systems. J. Eng. Math. 93, 41-60 (2015)
[6] Bai, Z.Z.: On spectral clustering of HSS preconditioner for generalized saddle-point matrices. Linear Algebra Appl. 555, 285-300 (2018)
[7] Bai, Z.Z.: Regularized HSS iteration methods for stabilized saddle-point problems. IMA J. Numer. Anal. 39(4), 1888-1923 (2019)
[8] Bai, Z.Z., Benzi, M.: Regularized HSS iteration methods for saddle-point linear systems. BIT Numer. Math. 57(2), 287-311 (2017)
[9] Bai, Z.Z., Golub, G.H.: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. IMA J. Numer. Anal. 27(1), 1-23 (2007)
[10] Bai, Z.Z., Golub, G.H., Pan, J.Y.: Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems. Numer. Math. 98(1), 1-32 (2004)
[11] Bai, Z.Z., Ng, M.K.: On inexact preconditioners for nonsymmetric matrices. SIAM J. Sci. Comput. 26(5), 1710-1724 (2005)
[12] Bai, Z.Z., Ng, M.K., Wang, Z.Q.: Constraint preconditioners for symmetric indefinite matrices. SIAM J. Matrix Anal. Appl. 31(2), 410-433 (2009)
[13] Bai, Z.Z., Pan, J.Y.: Matrix Analysis and Computations. SIAM, Philadelphia (2021)
[14] Bai, Z.Z., Parlett, B.N., Wang, Z.Q.: On generalized successive overrelaxation methods for augmented linear systems. Numer. Math. 102(1), 1-38 (2005)
[15] Bai, Z.Z., Wang, Z.Q.: On parameterized inexact Uzawa methods for generalized saddle point problems. Linear Algebra Appl. 428(11/12), 2900-2932 (2008)
[16] Beik, F.P.A., Benzi, M.: Iterative methods for double saddle point systems. SIAM J. Matrix Anal. Appl. 39(2), 902-921 (2018)
[17] Beik, F.P.A., Benzi, M.: Block preconditioners for saddle point systems arising from liquid crystal directors modeling. Calcolo 55(3), 29 (2018)
[18] Benzi, M., Deparis, S., Grandperrin, G., Quarteroni, A.: Parameter estimates for the relaxed dimensional factorization preconditioner and application to hemodynamics. Comput. Methods Appl. Mech. Eng. 300, 129-145 (2016)
[19] Benzi, M., Golub, G.H.: A preconditioner for generalized saddle point problems. SIAM J. Matrix Anal. Appl. 26(1), 20-41 (2005)
[20] Cao, Y., Li, S.: Block triangular preconditioners based on symmetric-triangular decomposition for generalized saddle point problems. Appl. Math. Comput. 358, 262-277 (2019)
[21] Chen, F., Ren, B.C.: On preconditioning of double saddle point linear systems arising from liquid crystal director modeling. Appl. Math. Lett. 136, 108445 (2023)
[22] Dollar, H.S.: Constraint-style preconditioners for regularized saddle-point problems. SIAM J. Matrix Anal. Appl. 29(2), 672-684 (2007)
[23] De Gennes, P.G., Prost, J.: The Physics of Liquid Crystals, 2nd edn. Clarendon Press, Oxford (1993)
[24] Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)
[25] Ipsen, I.C.F.: A note on preconditioning nonsymmetric matrices. SIAM J. Sci. Comput. 23(3), 1050-1051 (2001)
[26] Jiang, M.Q., Cao, Y.: On local Hermitian and skew-Hermitian splitting iteration methods for generalized saddle point problems. J. Comput. Appl. Math. 231(2), 973-982 (2009)
[27] Liang, Z.Z., Zhang, G.F.: Alternating positive semidefinite splitting preconditioners for double saddle point problems. Calcolo 56(3), 26 (2019)
[28] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM J. Sci. Comput. 21(6), 1969-1972 (2000)
[29] Pestana, J.: On the eigenvalues and eigenvectors of block triangular preconditioned block matrices. SIAM J. Matrix Anal. Appl. 35(2), 517-525 (2014)
[30] Ramage, A., Gartland, J.R.E.C.: A preconditioned nullspace method for liquid crystal director modeling. SIAM J. Sci. Comput. 35(1), B226-B247 (2013)
[31] Ren, B.C., Chen, F., Wang, X.L.: Improved splitting preconditioner for double saddle point problems arising from liquid crystal director modeling. Numer. Algorithms 91(3), 1363-1379 (2022)
[32] Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Philadelphia (2003)
[33] Shen, Q.Q., Shi, Q.: Generalized shift-splitting preconditioners for nonsingular and singular generalized saddle point problems. Comput. Math. Appl. 72(3), 632-641 (2016)
[34] Shen, S.Q.: A note on PSS preconditioners for generalized saddle point problems. Appl. Math. Comput. 237, 723-729 (2014)
[35] Simoncini, V.: Krylov subspace methods for saddle point problems with indefinite preconditioning. SIAM J. Matrix Anal. Appl. 24(2), 368-391 (2002)
[36] Stewart, I.W.: The Static and Dynamic Continuum Theory of Liquid Crystals: a Mathematical Introduction. Taylor and Francis, London (2004)
[37] Zhu, J.L., Wu, Y.J., Yang, A.L.: A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling. Numer. Algorithms 89(3), 987-1006 (2022)
