A fast, low memory cost, Krylov-space-based algorithm is proposed for the diagonalization of large Hamiltonian matrices required in time-dependent Hartree–Fock ~TDHF! and adiabatic time-dependent density-functional theory ~TDDFT! computations of electronic excitations. A deflection procedure based on the symplectic structure of the TDHF equations is introduced and its capability to find higher ...