  Band calculations for Ce compounds with the AuCu$_{3}$-type crystal structure
were carried out on the basis of dynamical mean field theory (DMFT). The
auxiliary impurity problem was solved by a method named NCA$f^{2}$vc
(noncrossing approximation including the $f^{2}$ state as a vertex correction).
The calculations take into account the crystal-field splitting, the spin-orbit
interaction, and the correct exchange process of the $f^{1} \rightarrow
f^{0},f^{2}$ virtual excitation. These are necessary features in the
quantitative band theory for Ce compounds and in the calculation of their
excitation spectra. The results of applying the calculation to CePd$_{3}$ and
CeRh$_{3}$ are presented as the first in a series of papers. The experimental
results of the photoemission spectrum (PES), the inverse PES, the
angle-resolved PES, and the magnetic excitation spectra were reasonably
reproduced by the first-principles DMFT band calculation. At low temperatures,
the Fermi surface (FS) structure of CePd$_{3}$ is similar to that of the band
obtained by the local density approximation. It gradually changes into a form
that is similar to the FS of LaPd$_{3}$ as the temperature increases, since the
$4f$ band shifts to the high-energy side and the lifetime broadening becomes
large.}
