Sternheimer equation - TDDFT.org

Linear solvers
Sparse: iteration with only matrix-vector products cheaper than inversion.
General advice: focus on preconditioner, not solver.
Use smoothing. But effective preconditioners are hard in real space
(especially in periodic systems).
Y Saad, Iterative methods for sparse linear systems (2000)
Krylov subspace methods
conjugate gradients (CG): Hermitian
biconjugate gradients (BiCG)
biconjugate gradients stabilized (BiCGSTAB)
quasi-minimal residual (QMR)
complex symmetric
general
symmetrized