  We revisit the problem of computing submatrices of the Cram\'er-Rao bound
(CRB), which lower bounds the variance of any unbiased estimator of a vector
parameter $\vth$. We explore iterative methods that avoid direct inversion of
the Fisher information matrix, which can be computationally expensive when the
dimension of $\vth$ is large. The computation of the bound is related to the
quadratic matrix program, where there are highly efficient methods for solving
it. We present several methods, and show that algorithms in prior work are
special instances of existing optimization algorithms. Some of these methods
converge to the bound monotonically, but in particular, algorithms converging
non-monotonically are much faster. We then extend the work to encompass the
computation of the CRB when the Fisher information matrix is singular and when
the parameter $\vth$ is subject to constraints. As an application, we consider
the design of a data streaming algorithm for network measurement.
