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

## 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.

- Authors:

- Fujian Normal University, School of Mathematics and Computer Science and FJKLMAA (China)

- Publication Date:

- OSTI Identifier:
- 22769324

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; DISTRIBUTION; EIGENVALUES; MATRICES; POLYNOMIALS

### Citation Formats

```
Ke, Yi-Fen, and Ma, Chang-Feng.
```*A low-order block preconditioner for saddle point linear systems*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0432-2.

```
Ke, Yi-Fen, & Ma, Chang-Feng.
```*A low-order block preconditioner for saddle point linear systems*. United States. doi:10.1007/S40314-017-0432-2.

```
Ke, Yi-Fen, and Ma, Chang-Feng. Tue .
"A low-order block preconditioner for saddle point linear systems". United States. doi:10.1007/S40314-017-0432-2.
```

```
@article{osti_22769324,
```

title = {A low-order block preconditioner for saddle point linear systems},

author = {Ke, Yi-Fen and Ma, Chang-Feng},

abstractNote = {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.},

doi = {10.1007/S40314-017-0432-2},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}

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