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.

Intro
SCHRÖDINGER EQUATION
NUMERICAL DISCRETIZATION
HAMILTONIAN MATRIX
FULL CONFIGURATION INTERACTION
FULL CI EIGENVALUE PROBLEM
OUTLINE
EDGE EIGENVALUE PROBLEM
EXACT LINE-SEARCH OF C
CDFCI COORDINATE DESCENT FULL CONEGURATION INTERACTION
ESTIMATOR OF EIGENVALUE
COMPLEXITY PER ITERATION
NUMERICAL EXAMPLE II - N2
Q IN ITERATION
UNROLL OFM
CONVERGENCE THEOREM
ACCELERATION TECHNIQUES
NUMERICAL RESULTS III FOR TRIOFM
CONCLUSION FUTURE WORK