Pose graphs have become a popular representation for solving the simultaneous localization and mapping (SLAM) problem. A pose graph is a set of robot poses connected by nonlinear constraints obtained from observations of features common to nearby poses. Optimizing large pose graphs has been a bottleneck for mobile robots, since the computation time of direct nonlinear optimization can grow cubically with the size of the graph. In this paper, we propose an efficient method for constructing and solving the linear subproblem, which is the bottleneck of these direct methods. We compare our method, called Sparse Pose Adjustment (SPA), with competing indirect methods, and show that it outperforms them in terms of convergence speed and accuracy. We demonstrate its effectiveness on a large set of indoor real-world maps, and a very large simulated dataset. Open-source implementations in C++, and the datasets, are publicly available.