| Title | Geometry-oblivious FMM for Compressing Dense SPD Matrices |
| Publication Type | Conference Paper |
| Year of Publication | 2017 |
| Authors | Yu, Chenhan D., Levitt, James, Reiz, Severin, Biros, George |
| Conference Name | Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis |
| Publisher | ACM |
| Conference Location | New York, NY, USA |
| ISBN Number | 978-1-4503-5114-0 |
| Keywords | composability, compressive sampling, Cyber-physical systems, fast matrix multiplication, fast multipole methods, geometry-oblivious, Heterogeneous computing, hierarchical matrices, privacy, pubcrawl, resilience, Resiliency |
| Abstract | We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, or "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in N log N or even N time, where N is the matrix size. Compression requires N log N storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices. |
| URL | http://doi.acm.org/10.1145/3126908.3126921 |
| DOI | 10.1145/3126908.3126921 |
| Citation Key | yu_geometry-oblivious_2017 |
Geometry-oblivious FMM for Compressing Dense SPD Matrices