  Weak lensing observations and supernova observations, combined with CMB
observations, can both provide powerful constraints on dark energy properties.
Considering statistical errors only, we find luminosity distances inferred from
2000 supernovae and large-scale (l < 1000) angular power spectra inferred from
redshift-binned cosmic shear maps place complementary constraints on w_0 and
w_a where w(z) = w_0 + w_a(a-1). Further, each set of observations can
constrain higher-dimensional parameterizations of w(z); we consider eigenmodes
of the w(z) error covariance matrix and find such datasets can each constrain
the amplitude of about 5 w(z) eigenmodes. We also consider another
parameterization of the dark energy.
