Recorded 17 April 2023. Xiantao Li of Pennsylvania State University presents "A stochastic algorithm for self-consistent calculations in DFT" at IPAM's workshop for Scale-Bridging Materials Modeling at Extreme Computational Scales. Abstract: The computation of electronic structures has recently become routine calculations in material science and chemistry. The dominating component in such calculations is the SCF iterations, mainly because of the eigenvalue problem. We present a stochastic approach, where the electronic density is formulated as a trace/diagonal of a matrix function, which is subsequently expressed as a statistical average. As a result, each SCF iteration only samples one random vector without having to compute all the orbitals. We present numerical results for both real-space and tight-binding discretizations. We also prove the convergence of the stochastic approach under mild conditions. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/workshop-ii-scale-bridging-materials-modeling-at-extreme-computational-scales/