# An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method

## Abstract

This paper is concerned with applying bandwidth and profile reduction reordering algorithms prior to computing an incomplete Cholesky factorization and using this as a preconditioner for the conjugate gradient method. Hundreds of reordering algorithms have been proposed to solve the problems of bandwidth and profile reductions since the mid-1960s. In previous publications, a large range of heuristics for bandwidth and/or profile reductions was reviewed. Based on this experience, 13 heuristics were selected as the most promising methods. These are evaluated in this paper along with a variant of the breadth-first search procedure that is proposed. Numerical results confirm the effectiveness of this modified reordering algorithm for linear systems derived from specific application areas. Moreover, the most promising heuristics for several application areas are identified when reducing the computational cost of the incomplete Cholesky-conjugate gradient method.

- Authors:

- Universidade Federal de Lavras (Brazil)

- Publication Date:

- OSTI Identifier:
- 22769288

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 3; 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; ALGORITHMS; FACTORIZATION; OPTIMIZATION; SYMMETRY

### Citation Formats

```
Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, Bernardes, J. A. B.,, and Chagas, G. O., E-mail: guilherme.chagas@computacao.ufla.br.
```*An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0490-5.

```
Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, Bernardes, J. A. B.,, & Chagas, G. O., E-mail: guilherme.chagas@computacao.ufla.br.
```*An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method*. United States. doi:10.1007/S40314-017-0490-5.

```
Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, Bernardes, J. A. B.,, and Chagas, G. O., E-mail: guilherme.chagas@computacao.ufla.br. Sun .
"An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method". United States. doi:10.1007/S40314-017-0490-5.
```

```
@article{osti_22769288,
```

title = {An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method},

author = {Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br and Bernardes, J. A. B., and Chagas, G. O., E-mail: guilherme.chagas@computacao.ufla.br},

abstractNote = {This paper is concerned with applying bandwidth and profile reduction reordering algorithms prior to computing an incomplete Cholesky factorization and using this as a preconditioner for the conjugate gradient method. Hundreds of reordering algorithms have been proposed to solve the problems of bandwidth and profile reductions since the mid-1960s. In previous publications, a large range of heuristics for bandwidth and/or profile reductions was reviewed. Based on this experience, 13 heuristics were selected as the most promising methods. These are evaluated in this paper along with a variant of the breadth-first search procedure that is proposed. Numerical results confirm the effectiveness of this modified reordering algorithm for linear systems derived from specific application areas. Moreover, the most promising heuristics for several application areas are identified when reducing the computational cost of the incomplete Cholesky-conjugate gradient method.},

doi = {10.1007/S40314-017-0490-5},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 3,

volume = 37,

place = {United States},

year = {2018},

month = {7}

}