SCHEDULE: NOV 12-18, 2011

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Parallel Reduction to Condensed Forms for Symmetric Eigenvalue Problems using Aggregated Fine-Grained and Memory-Aware Kernels

SESSION: Dense Linear Algebra

EVENT TYPE: Paper

TIME: 11:30AM - 12:00PM

AUTHOR(S):Azzam Haidar, Hatem Ltaief, Jack Dongarra

ROOM:TCC 305

ABSTRACT:
This paper introduces a novel implementation in reducing a symmetric dense matrix to tridiagonal form, which is the preprocessing step toward solving symmetric eigenvalue problems. Based on tile algorithms, the reduction follows a two-stage approach, where the tile matrix is first reduced to symmetric band form prior to the final condensed structure. The challenging trade-off between algorithmic performance and task granularity has been tackled through a grouping technique, which consists in aggregating fine-grained and memory-aware computational tasks during both stages, while sustaining the application overall high performance. A dynamic runtime environment system schedules then the different tasks in an out-of-order fashion. The performance for the tridiagonal reduction reported in this paper are unprecedented. Our implementation results in an up to 50-fold improvement (125 Gflop/s) compared to the equivalent routine from LAPACK and Intel MKL on an eight socket hexa-core AMD Opteron multicore shared-memory system with a matrix size of 24000x24000.

Chair/Author Details:

Azzam Haidar - University of Tennessee, Knoxville

Hatem Ltaief - KAUST Supercomputing Laboratory

Jack Dongarra - University of Tennessee, Knoxville

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The full paper can be found in the ACM Digital Library