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 blockJacobi 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 finegrained 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); 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 01678191
 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:https://doi.org/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:https://doi.org/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 blockJacobi 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 finegrained 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}
}
Web of Science
Works referencing / citing this record:
An efficient sparse approximate inverse preconditioning algorithm on GPU
journal, November 2019
 He, Guixia; Yin, Renjie; Gao, Jiaquan
 Concurrency and Computation: Practice and Experience, Vol. 32, Issue 7