Decentralized sequential hypothesis testing refers to a generalization of Wald's sequential hypothesis testing setup in which multiple decision makers make separate stopping decisions that are coupled through a common loss function. In the simplest such generalization, the stopping decisions are not seen by other decision makers. For this model, it is known that threshold-based stopping strategies are optimal. Two methods are presented for approximately computing the optimal thresholds. The first method, which is called orthogonal search, is an iterative method that approximately solves the coupled dynamic programs proposed in Teneketzis and Ho, Information and Computation, 1987. The second method, which is called direct search, approximates the performance of a threshold-based strategy and then searches over the thresholds using a derivative-free non-convex optimization algorithm. The approximations for both methods are based on discretizing the continuous-state information state process to a finite-state Markov chain and calculating the absorption probabilities and absorption stopping times for appropriately defined absorption sets. The performance of both the methods is compared numerically.