Non-monotonic recursive polynomial expansions for linear scaling calculation of the density matrix

Abstract

As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this paper, there is room for improvements. The key is to allow for non-monotonicity in the recursive polynomial expansion. Based on this idea, new purification schemes are proposed that require only half the number of matrix-matrix multiplications compared to previous schemes. The speedup is essentially independent of the location of the chemical potential and increases with decreasing band gap.

4 pages, 3 figures

References in corpus (1)

• Expansion algorithm for the density matrix

Cited by in corpus (8)

• Graph-based linear scaling electronic structure theory
• Extended Lagrangian free energy molecular dynamics
• Mixed Precision Fermi-Operator Expansion on Tensor Cores From a Machine Learning Perspective
• Parameterless stopping criteria for recursive density matrix expansions
• Graph-based Quantum Response Theory and Shadow Born-Oppenheimer Molecular Dynamics
• On-the-fly computation of frontal orbitals in density matrix expansions
• Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures
• Sparse approximate matrix-matrix multiplication for density matrix purification with error control