  Using quasiparticle self-consistent $GW$ calculations, we re-examined the
electronic structure of Sr$_2$RuO$_4$ and SrRuO$_3$. Our calculations show that
the correlation effects beyond the conventional LDA (local density
approximation) and GGA (generalized gradient approximation) are reasonably well
captured by QS$GW$ self-energy without any {\it ad hoc} parameter or any
ambiguity related to the double-counting and the downfolding issues. While the
spectral weight transfer to the lower and upper Hubbard band is not observed,
the noticeable bandwidth reduction and effective mass enhancement are obtained.
Important features in the electronic structures that have been debated over the
last decades such as the photoemission spectra at around $-3$ eV in
Sr$_2$RuO$_4$ and the half-metallicity for SrRuO$_3$ are discussed in the light
of our QS$GW$ results and in comparison with the previous studies. The
promising aspects of QS$GW$ are highlighted as the first-principles calculation
method to describe the moderately correlated 4$d$ transition metal oxides along
with its limitations.
