抄録
Linear algebra programs such as linear equation solvers and eigenvalue solvers have an inherent hierarchical structure; they are composed of calls to lower level computational routines such as inner product or matrixvector multiplication. Hence, one can predict their execution time by modeling the execution times of the lower level routines and accumulating them. Such hierarchical performance models can be used effectively for automatic performance tuning of linear algebra programs. In this paper, we survey recent studies along this line. In particular, we review several approaches for modeling the execution time of lower level routines, examine the conditions for the hierarchical tuning technique to be effective, and give an instance of linear algebra computation for which the technique is successful. We also discuss directions for future research, such as extension of the technique to deal with heterogeneous computing platforms, combination with algorithm generation techniques and incorporation into auto-tuning languages.
