Eigenvector-dependent nonlinear eigenvalue problems with affine-linear structures - (Ding LU, University of Kentucky)

21.06.2022 14:00 – 15:00

Eigenvector-dependent Nonlinear Eigenvalue Problems (NEPv) have long played critical roles in computational physics and chemistry and more recently become increasingly important in data science application. Practical NEPv usually has particular structures. In this talk, we consider a class of NEPv where the coefficient matrices pose a special affine-linear form. One important origin of such NEPv is the Rayleigh-quotient related optimization, including the trace-ratio optimization for dimension reduction and robust Rayleigh-quotient optimization for handling data uncertainties. We will establish variational characterizations of particular affine-linear NEPv, and then provide a geometric interpretation of a Self-Consistent Fields (SCF) iteration for solving the NEPv. The geometric interpretation reveals global convergence of SCF in many cases and explains its potential non-convergence issues in others. New improvements of SCF, including local acceleration schemes and global verification techniques are also discussed. Numerical experiments are provided to demonstrate the effectiveness of our approach.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

entrée libre