Abstract: Large dense matrices appear in many scientific computing and data analytics problems such as particle simulation and kernel methods. Rank-structured matrix representations are commonly used to reduce the quadratic multiplication and storage cost for dense matrices, and they are closely connected to fast algorithms such as FMM and FFT. However, their application usually requires expensive computation to represent a matrix in rank-structured format which involves compressing matrix blocks into low-rank form.
In this talk, I will discuss the study and application of a hybrid compression method, called the proxy point method, that can efficiently construct rank-structured matrix representations of dense matrices defined by kernel functions. Next, I will extend the applicability of rank-structured matrices and the proxy point method to help accelerate one main tensor contraction step in quantum chemistry (i.e., the Coulomb matrix construction). Lastly, I will discuss potential applications and extensions of rank-structured matrix techniques.