159
Views
6
CrossRef citations to date
0
Altmetric
Section B

A new preconditioner for generalized saddle point matrices with highly singular(1,1) blocks

Pages 2091-2101 | Received 14 Mar 2013, Accepted 17 Nov 2013, Published online: 26 Mar 2014

References

  • M. Benzi and G.H. Golub, A preconditioner for generalized saddle point problems, SIAM J. Matrix Anal. Appl. 26 (2004), pp. 20–41. doi: 10.1137/S0895479802417106
  • M. Benzi, G.H. Golub, and J. Liesen, Numerical solution of saddle point problems, Acta Numer. 14 (2005), pp. 1–137. doi: 10.1017/S0962492904000212
  • M. Benzi and J. Liu, Block preconditioning for saddle point systems with inde?nite (1, 1) block, Int. J. Comput. Math. 5 (2007), pp. 1–16.
  • M. Benzi and A.J. Wathen, Some preconditioning techniques for saddle point problems, Math. Indus. 13 (2008), pp. 195–211. doi: 10.1007/978-3-540-78841-6_10
  • Z.H. Cao, Augmentation block preconditioners for saddle point-type matrices with singular (1, 1) blocks, Num. Linear Algebra Appl. 15 (2008), pp. 515–533. doi: 10.1002/nla.572
  • Z.H. Cao, A note on spectrum analysis of augmentation block preconditioned generalized saddle point matrices, J. Comput. Appl. Math. 238(15) (2013), pp. 109–115. doi: 10.1016/j.cam.2012.08.024
  • C. Greif and D. Schötzau, Preconditioners for saddle point linear systems with highly singular (1, 1) blocks, Electron. Trans. Num. Anal. 22 (2006), pp. 114–121.
  • C. Greif and D. Schötzau, Preconditioners for the discretized time-harmonic Maxwell equations in mixed form, Num. Linear Algebra Appl. 14 (2007), pp. 281–297. doi: 10.1002/nla.515
  • E. Haber, U.M. Ascher, and D. Oldenberg, On the optimization techniques for solving non-linear inverse problems, Inverse Probl. 16 (2000), pp. 1263–1280. doi: 10.1088/0266-5611/16/5/309
  • T.Z. Huang, G.H. Cheng, and L. Li, New block triangular preconditioners for saddle point linear systems with highly singular (1,1) blocks, Math. Probl. Eng. 2009 (2009), 13 pp., Article ID 468965, doi: 10.1155/2009/468965.
  • P. Lancaster and M. Tismenetsky, The Theory of Matrices with applications, 2nd ed., Academic Press, London, 1985.
  • D. Li, C. Greif, and D. Schötzau, Parallel numerical solution of the time-harmonic Maxwell equations in mixed form, Num. Linear Algebra Appl. 19 (2012), pp. 525–539.
  • T. Rees and C. Greif, A preconditioner for linear systems arising from interior optimization methods, SIAM J. Sci. Comput. 29 (2007), pp. 1992–2007. doi: 10.1137/060661673
  • C. Siefert and E.D. Sturler, Preconditioners for generalized saddle-point problems, SIAM J. Numer. Anal. 44(3) (2006), pp. 1275–1296. doi: 10.1137/040610908
  • H.A. Van der Vorst, Iterative Krylov methods for large linear systems, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, UK, 2003.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.