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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
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.
Azzam Haidar - University of Tennessee, Knoxville
Hatem Ltaief - KAUST Supercomputing Laboratory
Jack Dongarra - University of Tennessee, Knoxville