We describe an iterative algorithm that converges to the maximum likelihood estimate of the position and intensity of a single fluorophore. Our technique efficiently computes and achieves the Cramér-Rao lower bound, an essential tool for parameter estimation. An implementation of the algorithm on graphics processing unit hardware achieved more than 10(5) combined fits and Cramér-Rao lower bound calculations per second, enabling real-time data analysis for super-resolution imaging and other applications.