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    Geostatistical Modeling and Prediction Using Mixed-Precision Tile Cholesky Factorization

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    Type
    Preprint
    Authors
    Abdulah, Sameh
    Ltaief, Hatem cc
    Sun, Ying cc
    Genton, Marc G. cc
    Keyes, David E. cc
    KAUST Department
    Extreme Computing Research Center
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Applied Mathematics and Computational Science Program
    Office of the President
    Date
    2020-01-08
    Permanent link to this record
    http://hdl.handle.net/10754/666233
    
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    Abstract
    Geostatistics represents one of the most challenging classes of scientific applications due to the desire to incorporate an ever increasing number of geospatial locations to accurately model and predict environmental phenomena. For example, the evaluation of the Gaussian log-likelihood function, which constitutes the main computational phase, involves solving systems of linear equations with a large dense symmetric and positive definite covariance matrix. Cholesky, the standard algorithm, requires O(n^3) floating point operators and has an O(n^2) memory footprint, where n is the number of geographical locations. Here, we present a mixed-precision tile algorithm to accelerate the Cholesky factorization during the log-likelihood function evaluation. Under an appropriate ordering, it operates with double-precision arithmetic on tiles around the diagonal, while reducing to single-precision arithmetic for tiles sufficiently far off. This translates into an improvement of the performance without any deterioration of the numerical accuracy of the application. We rely on the StarPU dynamic runtime system to schedule the tasks and to overlap them with data movement. To assess the performance and the accuracy of the proposed mixed-precision algorithm, we use synthetic and real datasets on various shared and distributed-memory systems possibly equipped with hardware accelerators. We compare our mixed-precision Cholesky factorization against the double-precision reference implementation as well as an independent block approximation method. We obtain an average of 1.6X performance speedup on massively parallel architectures while maintaining the accuracy necessary for modeling and prediction.
    Publisher
    arXiv
    arXiv
    2003.05324
    Additional Links
    https://arxiv.org/pdf/2003.05324
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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