  A comprehensive analysis of the Symanzik improved anisotropic
three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made.
Monte Carlo techniques are used to obtain numerical results for the static
potential, ratio of the renormalized and bare anisotropies, the string tension,
lowest glueball masses and the mass ratio. Evidence that rotational symmetry is
established more accurately for the Symanzik improved anisotropic action is
presented. The discretization errors in the static potential and the
renormalization of the bare anisotropy are found to be only a few percent
compared to errors of about 20-25% for the unimproved gauge action. Evidence of
scaling in the string tension, antisymmetric mass gap and the mass ratio is
observed in the weak coupling region and the behaviour is tested against
analytic and numerical results obtained in various other Hamiltonian studies of
the theory. We find that more accurate determination of the scaling
coefficients of the string tension and the antisymmetric mass gap has been
achieved, and the agreement with various other Hamiltonian studies of the
theory is excellent. The improved action is found to give faster convergence to
the continuum limit. Very clear evidence is obtained that in the continuum
limit the glueball ratio $M_{S}/M_{A}$ approaches exactly 2, as expected in a
theory of free, massive bosons.
