  One-sided dense matrix decompositions (e.g., Cholesky, LU, and QR) are the
key components in scientific computing in many different fields. Although their
design has been highly optimized for modern processors, they still consume a
considerable amount of energy. As CPU-GPU heterogeneous systems are commonly
used for matrix decompositions, in this work, we aim to further improve the
energy saving of one-sided matrix decompositions on CPU-GPU heterogeneous
systems. We first build an Algorithm-Based Fault Tolerance protected
overclocking technique (ABFT-OC) to enable us to exploit reliable overclocking
for key matrix decomposition operations. Then, we design an energy-saving
matrix decomposition framework, Bi-directional Slack Reclamation(BSR), that can
intelligently combine the capability provided by ABFT-OC and DVFS to maximize
energy saving and maintain performance and reliability. Experiments show that
BSR is able to save up to 11.7% more energy compared with the current best
energy saving optimization approach with no performance degradation and up to
14.1% Energy * Delay^2 reduction. Also, BSR enables the Pareto efficient
performance-energy trade-off, which is able to provide up to 1.43x performance
improvement without costing extra energy.
