Convergence of adaptive compression methods for Hartree-Fock-like equations
Provides theoretical guarantees for a widely used method in quantum physics, chemistry, and materials science.
The paper proves rigorous convergence properties of the adaptively compressed exchange (ACE) method for solving Hartree-Fock-like equations, establishing its reliability for linear eigenvalue problems.
The adaptively compressed exchange (ACE) method provides an efficient way for solving Hartree-Fock-like equations in quantum physics, chemistry, and materials science. The key step of the ACE method is to adaptively compress an operator that is possibly dense and full-rank. In this paper, we present a detailed study of the adaptive compression operation and establish rigorous convergence properties of the adaptive compression method in the context of solving linear eigenvalue problems. Our analysis also elucidates the potential use of the adaptive compression method in a wide range of problems.