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    Toward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem

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    Type
    Article
    Authors
    Haidar, Azzam
    Ltaief, Hatem cc
    Dongarra, Jack
    KAUST Department
    KAUST Supercomputing Laboratory (KSL)
    Date
    2012-01
    Permanent link to this record
    http://hdl.handle.net/10754/555650
    
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    Abstract
    Classical solvers for the dense symmetric eigenvalue problem suffer from the first step, which involves a reduction to tridiagonal form that is dominated by the cost of accessing memory during the panel factorization. The solution is to reduce the matrix to a banded form, which then requires the eigenvalues of the banded matrix to be computed. The standard divide and conquer algorithm can be modified for this purpose. The paper combines this insight with tile algorithms that can be scheduled via a dynamic runtime system to multicore architectures. A detailed analysis of performance and accuracy is included. Performance improvements of 14-fold and 4-fold speedups are reported relative to LAPACK and Intel's Math Kernel Library.
    Citation
    Toward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem 2012, 34 (6):C249 SIAM Journal on Scientific Computing
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Scientific Computing
    DOI
    10.1137/110823699
    Additional Links
    http://epubs.siam.org/doi/abs/10.1137/110823699
    ae974a485f413a2113503eed53cd6c53
    10.1137/110823699
    Scopus Count
    Collections
    Articles; KAUST Supercomputing Laboratory (KSL); KAUST Supercomputing Laboratory (KSL)

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