「Computing Matrix Functions on the K Computer」
In this talk, I will present a new, massively parallel library for computing the functions of sparse, Hermitian matrices. Matrix functions have a number of applications including materials science, the solution of partial differential equations, and the study of real world networks. One particularly important application is the development of linear scaling methods for quantum chemistry simulations. In this talk, I will review the theory of matrix functions, and discuss several methods of computation. Then I will present the parallelization strategy of our library, including the use of communication avoiding algorithms and task based MPI+OpenMP parallelization. I will discuss usability considerations, including how to build a library in Fortran which can be easily integrated into software written in many different programming languages. I will finish by presenting a number of different applications of this library, including quantum chemistry calculations on large biological molecules, social network analysis, and search engine optimization.
 Dawson, William, and Takahito Nakajima. "Massively parallel sparse matrix function calculations with NTPoly." Computer Physics Communications 225 (2018): 154-165.