Fast Algorithms for FCI Excited States - IPAM at UCLA
Explore a 46-minute conference talk on fast algorithms for Full Configuration Interaction (FCI) excited states presented by Yingzhou Li from Duke University at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Delve into unconstrained nonconvex optimization problems reformulating eigenvalue problems, with guaranteed global convergence to excited states. Examine linear convergence rates dependent on energy gaps, and learn about momentum acceleration, exact linesearch, and column locking techniques for improved efficiency. Discover the application of these algorithms to FCI matrices, covering topics such as the Schrödinger equation, numerical discretization, Hamiltonian matrix, and edge eigenvalue problems. Gain insights into complexity per iteration, convergence theorems, and acceleration techniques through numerical examples and results.