题目：New Analysis of SCF Iteration for Eigenvector-dependent Nonlinear Eigenvalue Problems
报告人：鲁玎 教授（University of Kentucky）
腾讯会议 ID： 485-651-298
Self-consistent field (SCF) iteration is a most general and widely-applied method for eigenvector-dependent nonlinear eigenvalue problems (NEPv). Despite simplicity, SCF is prone to slow convergence and may not converge at all. This has triggered considerable research in recent years for the convergence analysis of the algorithm. In this talk, we present some new results on the local convergence analysis of SCF. In the first part of the talk, we establish a sharp estimation of the local convergence factor of SCF for unitarily-invariant NEPv. This estimation allows us to prove the convergence of a level-shift scheme for fixing the divergence issue SCF. In the second part, we consider a class of NEPv without unitary invariance. We show that, at proper eigenbasis, such a problem can always be reformulated as an equivalent NEPv with unitary invariance. Then standard convergence analysis of SCF applies. Numerical experiments demonstrate the effectiveness of our approaches.