Free Access
Issue
ESAIM: M2AN
Volume 53, Number 5, September-October 2019
Page(s) 1607 - 1627
DOI https://doi.org/10.1051/m2an/2019029
Published online 09 August 2019
  1. I.S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equation. Rev. Modern Phys. 74 (2002) 99. [CrossRef] [Google Scholar]
  2. S.R. Arridge, Optical tomography in medical imaging. Inverse Prob. 15 (1999) 41–93. [CrossRef] [Google Scholar]
  3. O. Axelsson and A. Kucherov, Real valued iterative methods for solving complex symmetric linear systems. Numer. Linear Algebra Appl. 7 (2000) 197–218. [CrossRef] [Google Scholar]
  4. O. Axelsson, M. Neytcheva and B. Ahmad, A comparison of iterative methods to solve complex valued linear algebraic systems. Numer. Algor. 66 (2014) 811–841. [CrossRef] [Google Scholar]
  5. Z.-Z. Bai, On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems. Computing 89 (2010) 171–197. [CrossRef] [Google Scholar]
  6. Z.-Z. Bai, Block preconditioners for elliptic PDE-constrained optimization problems. Computing 91 (2011) 379–395. [CrossRef] [Google Scholar]
  7. Z.-Z. Bai, Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks. J. Comput. Appl. Math. 237 (2013) 295–330. [CrossRef] [Google Scholar]
  8. Z.-Z. Bai, M. Benzi and F. Chen, Modified HSS iteration methods for a class of complex symmetric linear systems. Computing 87 (2010) 93–111. [CrossRef] [Google Scholar]
  9. Z.-Z. Bai, M. Benzi and F. Chen, On preconditioned MHSS iteration methods for complex symmetric linear systems. Numer. Algor. 56 (2011) 297–317. [CrossRef] [Google Scholar]
  10. Z.-Z. Bai, M. Benzi, F. Chen and Z.-Q. Wang, 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 (2013) 343–369. [CrossRef] [Google Scholar]
  11. 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) 603–626. [CrossRef] [Google Scholar]
  12. Z.-Z. Bai, G.H. Golub and J.-Y. Pan, Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems. Numer. Math. 98 (2004) 1–32. [CrossRef] [Google Scholar]
  13. Z.-Z. Bai, G.H. Golub and C.-K. Li, Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Math. Comput. 76 (2007) 287–298. [CrossRef] [Google Scholar]
  14. M. Benzi, Preconditioning techniques for large linear systems: a survey. J. Comput. Phys. 182 (2002) 418–477. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Benzi, D. Bertaccini, Block preconditioning of real-valued iterative algorithms for complex linear systems. IMA. J. Numer. Anal 28 (2008) 598–618. [CrossRef] [Google Scholar]
  16. M. Benzi, G.H. Golub and J. Liesen, Numerical solution of saddle point problems. Acta Numer. 14 (2005) 1–137. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Berman and R.J. Plemmons, Non-negative Matrices in the Mathematical Sciences, 2nd edition. SIAM, Philadephia (1994). [CrossRef] [Google Scholar]
  18. D. Bertaccini, Efficient solvers for sequences of complex symmetric linear systems. Electron. Trans. Numer. Anal. 18 (2004) 49–64. [Google Scholar]
  19. Z. Chao and G.-L. Chen, A generalized modified HSS method for singular complex symmetric linear systems. Numer. Algor. 73 (2016) 77–89. [CrossRef] [Google Scholar]
  20. F. Chen and Q.-Q. Liu, On semi-convergence of modified HSS iteration methods. Numer. Algor. 64 (2013) 507–518. [CrossRef] [Google Scholar]
  21. C.-R. Chen and C.-F. Ma, AOR-Uzawa iterative method for a class of complex symmetric linear system of equations. Comput. Math. Appl. 72 (2016) 2462–2472. [CrossRef] [Google Scholar]
  22. M. Dehghan, M. Dehghani-Madiseh and M. Hajarian, A generalized preconditioned MHSS method for a class of complex symmetric linear systems. Math. Model. Anal. 18 (2013) 561–576. [CrossRef] [Google Scholar]
  23. A. Feriani, F. Perotti and V. Simoncini, Iterative system solvers for the frequency analysis of linear mechanical systems. Comput. Methods Appl. Mech. Engrg. 190 (2000) 1719–1739. [CrossRef] [Google Scholar]
  24. R.W. Freund, Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices. SIAM J. Sci. Stat. Comput. 13 (1992) 425–448. [CrossRef] [Google Scholar]
  25. A. Frommer, T. Lippert, B. Medeke and K. Schilling, Numerical challenges in lattice quantum chromodynamics. Lecture Notes Comput. Sci. Eng. 15 (2000) 1719–1739. [Google Scholar]
  26. L. Guo, L. Liu and Y. Wu, Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions. Non-linear Anal. Model. Control 21 (2015) 635–650. [CrossRef] [Google Scholar]
  27. M. Han, X. Hou, L. Sheng and C. Wang, Theory of rotated equations and applications to a population model. Discrete Cont. Dyn. Syst. -A 38 (2018) 2171–2185. [CrossRef] [Google Scholar]
  28. M. Han, L. Sheng and X. Zhang, Bifurcation theory for finitely smooth planar autonomous differential systems. J. Differ. Equ. 264 (2018) 3596–3618. [CrossRef] [Google Scholar]
  29. M.R. Hestenes and E.L. Stiefel. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stand. Sec. B 49 (1952) 409–436. [CrossRef] [MathSciNet] [Google Scholar]
  30. D. Hezari, V. Edalatpour and D.K. Salkuyeh, Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations. Numer. Linear Algebra Appl. 22 (2015) 761–776. [CrossRef] [Google Scholar]
  31. D. Hezari, D.K. Salkuyeh and V. Edalatpour, A new iterative method for solving a class of complex symmetric system of linear equations. Numer. Algor. 73 (2016) 927–955. [CrossRef] [Google Scholar]
  32. F. Li and G. Du, General energy decay for a degenerate viscoelastic Petrovsky-type plate equation with boundary feedback. J. Appl. Anal. Comput. 8 (2018) 390–401. [Google Scholar]
  33. C.-L. Li and C.-F. Ma, On Euler-extrapolated Hermitian/skew-Hermitian splitting method for complex symmetric linear systems. Appl. Math. Lett. 86 (2018) 42–48. [CrossRef] [Google Scholar]
  34. C.-L. Li and C.-F. Ma, Efficient parameterized rotated shift-splitting preconditioner for a class of complex symmetric linear systems. Numer. Algor. 80 (2019) 337–354. [CrossRef] [Google Scholar]
  35. C.-L. Li and C.-F. Ma, On semi-convergence of parameterized SHSS method for a class of singular complex symmetric linear systems. Comput. Math. Appl. 77 (2019) 466–475. [CrossRef] [Google Scholar]
  36. M. Li and J. Wang, Exploring delayed mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations. Appl. Math. Comput. 324 (2018) 254–265. [Google Scholar]
  37. C.-X. Li and S.-L. Wu, A single-step HSS method for non-Hermitian positive definite linear systems. Appl. Math. Lett. 44 (2015) 26–29. [CrossRef] [Google Scholar]
  38. Q.-H. Liu and A.-J. Liu, Block SOR methods for the solution of indefinite least squares problems. Calcolo 51 (2014) 367–379. [CrossRef] [Google Scholar]
  39. G. Moro and J.H. Freed, Calculation of ESR spectra and related FokkerPlanck forms by the use of the Lanczos algorithm. J. Chem. Phys. 74 (1981) 3757–3773. [CrossRef] [Google Scholar]
  40. B. Poirier, Effecient preconditioning scheme for block partitioned matrices with structured sparsity. Numer. Linear Algebra Appl. 7 (2000) 715–726. [CrossRef] [Google Scholar]
  41. B. Qu, B.-H. Liu and N. Zheng, On the computation of the step-size for the CQ-like algorithms for the split feasibility problem. Appl. Math. Comput. 262 (2015) 218–223. [Google Scholar]
  42. L. Reichel and Q. Ye, Breakdown-free GMRES for singular systems. SIAM J. Matrix Anal. Appl. 26 (2005) 1001–1021. [CrossRef] [Google Scholar]
  43. L. Ren and J. Xin, Almost global existence for the Neumann problem of quasilinear wave equations outside star-shaped domains in 3D. Electron. J. Differ. Equ. 312 (2018) 1–22. [Google Scholar]
  44. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS Press, New York (1995). [Google Scholar]
  45. Y. Saad and M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (1986) 856–869. [CrossRef] [MathSciNet] [Google Scholar]
  46. D.K. Salkuyeh, D. Hezari and V. Edalatpour, Generalized successive overrelaxation iterative method for a class of complex symmetric linear system of equations. Int. J. Comput. Math. 92 (2015) 802–815. [CrossRef] [Google Scholar]
  47. D. Schmitt, B. Steffen and T. Weiland, 2D and 3D computations of lossy eigenvalue problems. IEEE Trans. Magn. 30 (1994) 3578–3581. [CrossRef] [Google Scholar]
  48. H. Tian and M. Han, Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems. J. Differ. Equ. 263 (2017) 7448–7474. [CrossRef] [Google Scholar]
  49. B. Wang, Exponential Fourier collocation methods for solving first-order differential equations. J. Comput. Appl. Math. 35 (2017) 711–736. [Google Scholar]
  50. B. Wang, F. Meng and Y. Fang, Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations. Appl. Numer. Math. 119 (2017) 164–178. [CrossRef] [Google Scholar]
  51. B. Wang, X. Wu and F. Meng, Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second order differential equations. J. Comput. Appl. Math. 313 (2017) 185–201. [CrossRef] [Google Scholar]
  52. S.-L. Wu and C.-X. Li, On semi-convergence of modified HSS method for a class of complex singular linear systems. Appl. Math. Lett. 38 (2014) 57–60. [CrossRef] [Google Scholar]
  53. M.-L. Zeng and C.-F. Ma, A parameterized SHSS iteration method for a class of complex symmetric system of linear equations. Comput. Math. Appl. 71 (2016) 2124–2131. [CrossRef] [Google Scholar]
  54. M.-L. Zeng and G.-F. Zhang, Complex-extrapolated MHSS iteration method for singular complex symmetric linear systems. Numer. Algor. 76 (2017) 1021–1037. [CrossRef] [Google Scholar]

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