  We introduce a semistochastic implementation of the power method to compute,
for very large matrices, the dominant eigenvalue and expectation values
involving the corresponding eigenvector. The method is semistochastic in that
the matrix multiplication is partially implemented numerically exactly and
partially with respect to expectation values only. Compared to a fully
stochastic method, the semistochastic approach significantly reduces the
computational time required to obtain the eigenvalue to a specified statistical
uncertainty. This is demonstrated by the application of the semistochastic
quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard
model and the carbon dimer.
