Before revision:  For the latter (continuous) we derive a gradient descent algorithm to project from the ambient space of covariance matrices to wald space and for both we derive computational methods to compute geodesics in polynomial time and show numerically that the two information geometries (discrete and continuous) are very similar.
After revision:  For the latter (continuous) we derive a gradient descent algorithm to project from the ambient space of covariance matrices to wald space . For both geometries we derive computational methods to compute geodesics in polynomial time and show numerically that the two information geometries (discrete and continuous) are very similar.