Exploiting the Error Resilience of the Preconditioned Conjugate Gradient Method for Energy and Delay Optimization

The Preconditioned Conjugate Gradient (PCG) method is well-established for solving linear equations. Running the PCG method on a hardware accelerator ensures fast and efficient computation. At the same time, each hardware accelerator may be slightly different due to process variability or aging. To handle the variability, a rather pessimistic frequency selection for the whole population of accelerators is often utilized. Increasing the frequency may improve the performance but may also increase the risk of computational errors, affect the convergence of PCG or even corrupt the PCG results. In this paper, we present a method to determine the frequency for each hardware accelerator instance which optimizes the execution time and the energy efficiency of the PCG method. First, a technique is presented to analyze the error resilience of a PCG algorithm to overclocking. Based on the analysis results, we increase the frequency to speed up the convergence while keeping the error rate below the required threshold.