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    An Empirical Analysis of the Performance of Preconditioners for SPD Systems

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    Type
    Article
    Authors
    George, Thomas
    Gupta, Anshul
    Sarin, Vivek
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2012-08-01
    Permanent link to this record
    http://hdl.handle.net/10754/597521
    
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    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.
    Sponsors
    This work was partly supported by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Association for Computing Machinery (ACM)
    Journal
    ACM Transactions on Mathematical Software
    DOI
    10.1145/2331130.2331132
    ae974a485f413a2113503eed53cd6c53
    10.1145/2331130.2331132
    Scopus Count
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