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

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SIAM Journal on Scientific Computing, ISSN: 1064-8275, Vol: 34, Issue: 6, Page: C249-C274

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Haidar, Azzam; Ltaief, Hatem; Dongarra, Jack
Society for Industrial & Applied Mathematics (SIAM); Society for Industrial and Applied Mathematics
Mathematics; divide and conquer; symmetric eigenvalue solver; tile algorithms; dynamic scheduling
article description
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. © 2012 Society for Industrial and Applied Mathematics.