Sparse approximate matrix-matrix multiplication for density matrix purification with error control

TL;DR

This paper introduces a new method for sparse approximate matrix multiplication with strict error control, optimized for parallel electronic structure calculations, ensuring accuracy and efficiency.

Contribution

It presents a novel error control scheme combined with parameter tuning for sparse matrix multiplication, implemented within a parallel programming model.

Findings

Effective error control in sparse matrix multiplication demonstrated

Improved performance in parallel density matrix purification

Achieves linear scaling in electronic structure calculations

Abstract

We propose a method for strict error control in sparse approximate matrix-matrix multiplication. The method combines an error bound and a parameter sweep to select an appropriate threshold value. The scheme for error control and the sparse approximate multiplication are implemented using the Chunks and Tasks parallel programming model. We demonstrate the performance of the method in parallel linear scaling electronic structure calculations using density matrix purification with rigorous error control.