We accelerate the time-consuming iterations for projective reconstruction, a key component of self-calibration for computing 3-D shapes from feature point tracking over a video sequence. We first summarize the algorithms of the primal and dual methods for projective reconstruction. Then, we replace the eigenvalue computation in each step by the power method. We also accelerate the power method itself. Furthermore, we introduce the SOR method for accelerating the subspace fitting involved in the iterations. Using simulated and real video images, we demonstrate that the computation sometimes becomes several thousand times faster.