BIT Numerical Mathematics

, Volume 56, Issue 2, pp 489–500 | Cite as

Spectrum analysis of a more general augmentation block preconditioner for generalized saddle point matrices

  • Yi-Fen Ke
  • Chang-Feng Ma


In this paper, some errors are pointed out and the correct results are given for the paper Axelsson et al. (J Comput Appl Math 280:141–157, 2015). Then, a class of general augmentation block preconditioners for solving generalized saddle point systems with singular (1, 1) blocks are considered. Results concerning the eigenvalue distribution and forms of the eigenvectors of the preconditioned generalized saddle point matrix are presented. These results extend previous one in the literature.


Generalized saddle point matrix Preconditioner Eigenvalue Clustering 

Mathematics Subject Classification

65F10 65F50 15A24 



The authors would like to thank the anonymous reviewers for their comments that helped to improve the presentation of this paper.


  1. 1.
    Axelsson, O., Blaheta, R., Byczanski, P., Karátson, J., Ahmad, B.: Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems. J. Comput. Appl. Math. 280, 141–157 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Cao, Z.-H.: A note on spectrum analysis of augmentation block preconditioned generalized saddle point matrices. J. Comput. Appl. Math. 238, 109–115 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Greif, C., Schötzau, D.: Preconditioners for saddle point linear systems with highly singular (1, 1) blocks. Electron. Trans. Numer. Anal. 22, 114–121 (2006)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Rees, T., Greif, C.: A preconditioner for linear systems arising from interior optimization methods. SIAM J. Sci. Comput. 29, 1992–2007 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Cao, Z.-H.: Augmentation block preconditioners for saddle point-type matrices with singular (1, 1) blocks. Numer. Linear Algebra Appl. 15, 515–533 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gantmacher, F.R.: The Theory of Matrices. Chelsea Publishing Company, New York (1959)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceFujian Normal UniversityFuzhouPeople’s Republic of China

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