R. Yokota, H. Ibeid, D.E. Keyes
In "Proceedings of the International Workshop on Eigenvalue Problems: Algorithms, Software and Applications, in Petascale Computing" (EPASA'15), T. Sakurai et al., eds., (2016)
There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.