An Empirical Analysis of the Performance of Preconditioners for SPD Systems

Handle URI:
http://hdl.handle.net/10754/597521
Title:
An Empirical Analysis of the Performance of Preconditioners for SPD Systems
Authors:
George, Thomas; Gupta, Anshul; Sarin, Vivek
Abstract:
Preconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent, but also fairly sensitive to the choice of their tunable parameters. As a result, a typical practitioner is faced with an overwhelming number of choices of solvers, preconditioners, and their parameters. The diversity of preconditioners makes it difficult to analyze them in a unified theoretical model. A systematic empirical evaluation of existing preconditioned iterative solvers can help in identifying the relative advantages of various implementations. We present the results of a comprehensive experimental study of the most popular preconditioner and iterative solver combinations for symmetric positive-definite systems. We introduce a methodology for a rigorous comparative evaluation of various preconditioners, including the use of some simple but powerful metrics. The detailed comparison of various preconditioner implementations and a state-of-the-art direct solver gives interesting insights into their relative strengths and weaknesses. We believe that these results would be useful to researchers developing preconditioners and iterative solvers as well as practitioners looking for appropriate sparse solvers for their applications. © 2012 ACM.
Citation:
George T, Gupta A, Sarin V (2012) An Empirical Analysis of the Performance of Preconditioners for SPD Systems. TOMS 38: 1–30. Available: http://dx.doi.org/10.1145/2331130.2331132.
Publisher:
Association for Computing Machinery (ACM)
Journal:
ACM Transactions on Mathematical Software
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
1-Aug-2012
DOI:
10.1145/2331130.2331132
Type:
Article
ISSN:
0098-3500
Sponsors:
This work was partly supported by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorGeorge, Thomasen
dc.contributor.authorGupta, Anshulen
dc.contributor.authorSarin, Viveken
dc.date.accessioned2016-02-25T12:41:21Zen
dc.date.available2016-02-25T12:41:21Zen
dc.date.issued2012-08-01en
dc.identifier.citationGeorge T, Gupta A, Sarin V (2012) An Empirical Analysis of the Performance of Preconditioners for SPD Systems. TOMS 38: 1–30. Available: http://dx.doi.org/10.1145/2331130.2331132.en
dc.identifier.issn0098-3500en
dc.identifier.doi10.1145/2331130.2331132en
dc.identifier.urihttp://hdl.handle.net/10754/597521en
dc.description.abstractPreconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent, but also fairly sensitive to the choice of their tunable parameters. As a result, a typical practitioner is faced with an overwhelming number of choices of solvers, preconditioners, and their parameters. The diversity of preconditioners makes it difficult to analyze them in a unified theoretical model. A systematic empirical evaluation of existing preconditioned iterative solvers can help in identifying the relative advantages of various implementations. We present the results of a comprehensive experimental study of the most popular preconditioner and iterative solver combinations for symmetric positive-definite systems. We introduce a methodology for a rigorous comparative evaluation of various preconditioners, including the use of some simple but powerful metrics. The detailed comparison of various preconditioner implementations and a state-of-the-art direct solver gives interesting insights into their relative strengths and weaknesses. We believe that these results would be useful to researchers developing preconditioners and iterative solvers as well as practitioners looking for appropriate sparse solvers for their applications. © 2012 ACM.en
dc.description.sponsorshipThis work was partly supported by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.subjectIterative solversen
dc.subjectNumerical softwareen
dc.subjectPreconditionersen
dc.subjectSparse linear systemsen
dc.titleAn Empirical Analysis of the Performance of Preconditioners for SPD Systemsen
dc.typeArticleen
dc.identifier.journalACM Transactions on Mathematical Softwareen
dc.contributor.institutionInternational Business Machines, Armonk, United Statesen
dc.contributor.institutionIBM Thomas J. Watson Research Center, Yorktown Heights, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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