High-performance Randomized Matrix Computations for Big Data Analytics and Applications
概要
We are developing random sketching algorithms with high-performance implementations on supercomputers to compute singular value decomposition (SVD) and linear system (LS) solutions of very large-scale matrices. Few numerical solvers, especially randomized algorithms, are designed to tackle very large-scale matrix computations on the latest supercomputers. . We intend to develop efficient sketching schemes to compute approximate SVD and LS solutions of large-scale matrices. The main idea is to sketch the matrices by randomized algorithms to reduce the computational dimensions and then suitably integrate the sketches to improve the accuracy and to lower the computational costs. We intend to implement the proposed algorithms on supercomputers. One essential component of this project is to develop effective automatic software auto-tuning (AT) technologies, so that the package can fully take advantage of the computational capabilities of the target supercomputers that include CPU homogeneous and CPU-GPU heterogeneous parallel computers.