  Inspired by Grimme's simplified Tamm-Dancoff density functional theory
approach [S. Grimme, J. Chem. Phys. \textbf{138}, 244104 (2013)], we describe a
simplified approach to excited state calculations within the GW approximation
to the self-energy and the Bethe-Salpeter equation (BSE), which we call
sGW/sBSE. The primary simplification to the electron repulsion integrals yields
the same structure as with tensor hypercontraction, such that our method has a
storage requirement that grows quadratically with system size and computational
timing that grows cubically with system size. The performance of sGW is tested
on the ionization potential of the molecules in the GW100 test set, for which
it differs from \textit{ab intio} GW calculations by only 0.2 eV. The
performance of sBSE (based on sGW input) is tested on the excitation energies
of molecules in the Thiel set, for which it differs from \textit{ab intio}
GW/BSE calculations by about 0.5 eV. As examples of the systems that can be
routinely studied with sGW/sBSE, we calculate the band gap and excitation
energy of hydrogen-passivated silicon nanocrystals with up to 2650 electrons in
4678 spatial orbitals and the absorption spectra of two large organic dye
molecules with hundreds of atoms.
