A Smart Tuning Strategy for Restart Frequency of GMRES(m) with Hierarchical Cache Sizes

摘要

In this paper, we propose a smart tuning strategy that uses the cache size hierarchy of current multicore architectures. Both increase and decrease auto-tuning (AT) strategies for the restart frequency of GMRES(m) (Generalized Minimum Residual) are evaluated with the proposed hierarchical cache sizes. This evaluation, using one node of the T2K Open Supercomputer (Univ. Tokyo), demonstrates that the proposed strategies are very efficient compared to previous strategies without hierarchical cache sizes. We test both strategies with 22 matrices from the University of Florida Sparse Matrix Collection. As a result, we find an average speedup of 1.13× (maximum 2.06×) using an increase strategy (an implementation of Xabclib), and an average speedup of 4.25× (maximum 15.1×) with a decrease strategy (Aquilanti's) using the proposed method.