# Incomplete Sparse Approximate Inverses for Parallel Preconditioning

## Abstract

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as an attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.

- Authors:

- Karlsruhe Inst. of Technology (KIT) (Germany); Univ. of Tennessee, Knoxville, TN (United States). Innovative Computing Lab.
- Technical Univ. of Munich (Germany). Dept. of Informatics
- Univ. of Tennessee, Knoxville, TN (United States). Innovative Computing Lab.; Univ. of Manchester (United Kingdom). School of Computer Science; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Univ. of Tennessee, Knoxville, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1407456

- Alternate Identifier(s):
- OSTI ID: 1511776

- Grant/Contract Number:
- SC0016513

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Parallel Computing

- Additional Journal Information:
- Journal Volume: 71; Journal ID: ISSN 0167-8191

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; preconditioning; incomplete sparse approximate inverse; incomplete LU factorization; approximate sparse triangular solves; parallel computing

### Citation Formats

```
Anzt, Hartwig, Huckle, Thomas K., Bräckle, Jürgen, and Dongarra, Jack. Incomplete Sparse Approximate Inverses for Parallel Preconditioning. United States: N. p., 2017.
Web. doi:10.1016/j.parco.2017.10.003.
```

```
Anzt, Hartwig, Huckle, Thomas K., Bräckle, Jürgen, & Dongarra, Jack. Incomplete Sparse Approximate Inverses for Parallel Preconditioning. United States. doi:10.1016/j.parco.2017.10.003.
```

```
Anzt, Hartwig, Huckle, Thomas K., Bräckle, Jürgen, and Dongarra, Jack. Sat .
"Incomplete Sparse Approximate Inverses for Parallel Preconditioning". United States. doi:10.1016/j.parco.2017.10.003. https://www.osti.gov/servlets/purl/1407456.
```

```
@article{osti_1407456,
```

title = {Incomplete Sparse Approximate Inverses for Parallel Preconditioning},

author = {Anzt, Hartwig and Huckle, Thomas K. and Bräckle, Jürgen and Dongarra, Jack},

abstractNote = {In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as an attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.},

doi = {10.1016/j.parco.2017.10.003},

journal = {Parallel Computing},

number = ,

volume = 71,

place = {United States},

year = {2017},

month = {10}

}

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