A relaxed block-triangular splitting preconditioner for generalized saddle-point problems

ABSTRACT

For the generalized saddle-point problems, based on a new block-triangular splitting of the saddle-point matrix, we introduce a relaxed block-triangular splitting preconditioner to accelerate the convergence rate of the Krylov subspace methods. This new preconditioner is easily implemented since it has simple block structure. The spectral property of the preconditioned matrix is analysed. Moreover, the degree of the minimal polynomial of the preconditioned matrix is also discussed. Numerical experiments are reported to show the preconditioning effect of the new preconditioner.

KEYWORDS:

• Generalized saddle-point problem
• preconditioner
• matrix splitting
• spectral property
• minimal polynomial

2010 AMS SUBJECT CLASSIFICATIONS:

• 65F08
• 65F10
• 76D05

Acknowledgements

The authors are very much indebted to the referees for providing very useful comments and suggestions, which greatly improved the original manuscript of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [Grant Nos. 11401281, 11471150] and the Fundamental Research Fund for the Central Universities [Grant No. lzujbky-2016-97].