SCHEDULE: NOV 10-16, 2012
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A Scalable, Numerically Stable, High-Performance Tridiagonal Solver Using GPUs
SESSION: Maximizing Performance on Multi-Core and Many-Core Architectures
EVENT TYPE: Papers
TIME: 2:00PM - 2:30PM
SESSION CHAIR: Atsushi Hori
AUTHOR(S):Li-Wen Chang, John A. Stratton, Hee-Seok Kim, Wen-Mei W. Hwu
In this paper, we present a scalable, numerically stable, high-performance tridiagonal solver. The solver is based on the SPIKE algorithm, a method for partitioning a large matrix into small independent matrices, which can be solved in parallel. For each small matrix, our solver applies a general 1-by-1 or 2-by-2 diagonal pivoting algorithm, which is known to be numerically stable. Our paper makes two major contributions. First, our solver is the first numerically stable tridiagonal solver for GPUs. Our solver provides comparable quality of stable solutions to Intel MKL and Matlab, at speed comparable to the GPU tridiagonal solvers in existing packages like NVIDIA CUSPARSE. It is also scalable to multiple GPUs and CPUs. Second, we present and analyze two key optimization strategies for our solver: a high-throughput data layout transformation for memory efficiency, and a dynamic tiling approach for reducing the memory access footprint caused by branch divergence.
Atsushi Hori (Chair) - RIKEN
Li-Wen Chang - University of Illinois at Urbana-Champaign
John A. Stratton - University of Illinois at Urbana-Champaign
Hee-Seok Kim - University of Illinois at Urbana-Champaign
Wen-Mei W. Hwu - University of Illinois at Urbana-Champaign