# A low-order block preconditioner for saddle point linear systems

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## Abstract

A preconditioner is proposed for the large and sparse linear saddle point problems, which is based on a low-order three-by-three block saddle point form. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial for the preconditioned matrix are discussed. Numerical results show that the optimal convergence behavior can be achieved when the new preconditioner is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.

### Keywords

Saddle point problem Preconditioner Eigenvalue distribution### Mathematics Subject Classification

65F10 65F08 65F50## Notes

### Acknowledgements

The authors would like to express their great thankfulness to the referees for the comments and constructive suggestions very much, which are valuable in improving the quality of the original paper.

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