Sauve and Fessler , \ Recursive Algorithms for Computing the Cr Bound

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this note we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient algorithms. For a large class of inverse problems we show that non-monotone Gauss-Seidel and preconditioned conjugate gradient algorithms require signi cantly fewer ops for convergence than monotone \bound preserving" algorithms.