Minimization principles of linear response eigenvalue problems

Zhaojun Bai
University of California, Davis

Linear Response (LR) eigenvalue problems arise from excitation state
calculations in the study of collective motion of many particle
systems. There are a great deal of recent work and interests in
developing efficient simulation techniques for excitation state
calculations of molecules for materials design in energy science.
In this talk, we will first present minimization principles of
LR eigenvalue problems and then discuss the development of
conjugate gradient-like algorithms for simultaneously computing the
smallest eigenvalues with positive sign.  Finally, we
present numerical results of large-scale LR eigenproblems
for calculating excitation states of molecules.

This is a joint work with Ren-cang Li, Dario Rocca and Giulia Galli.