  We present recent theoretical results on superconductivity in
correlated-electron systems, especially in the two-dimensional Hubbard model
and the three-band d-p model. The mechanism of superconductivity in
high-temperature superconductors has been extensively studied on the basis of
various electronic models and also electron-phonon models. In this study we
investigate the properties of superconductivity in correlated-electron systems
by using numerical methods such as the variational Monte Carlo method and the
quantum Monte Carlo method.
  The Hubbard model is one of basic models for strongly correlated electron
systems, and is regarded as the model of cuprate high temperature
superconductors. The d-p model is more realistic model for cuprates. The
superconducting condensation energy obtained by adopting the Gutzwiller ansatz
is in reasonable agreement with the condensation energy estimated for
YBa_2Cu_3O_7. We show the phase diagram of the ground state using this method.
We have further investigated the stability of striped and checkerboard states
in the under-doped region. The relationship of the hole density x and
incommensurability \delta, \delta\sim x, is satisfied in the lower doping
region, as indicated by the variational Monte Carlo calculations. We have
performed a variational Monte Carlo simulation on a two-dimensional t-t'-t"-U
Hubbard model with a Bi-2212 type band structure and found that the 4\times 4
period checkerboard spin modulation, that is characterized by multi Q vectors,
is stabilized.
  We also present a new algorithm of the diagonalization quantum Monte Carlo
method that is a method for the evaluation of expectation values without the
negative sign difficulty. We show that the pair correlation function is not
enhanced at half-filling, and is indeed enhanced with hole doping.
