Dynamic programming with Hermite approximation

Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions over continuous states. Hermite data can be easily obtained from solving the Bellman equation and used to approximate the value functions. We illustrate the use of Hermite data with one-, three-, and six-dimensional examples. We find that Hermite approximation improves the accuracy in value function iteration (VFI) by one to three digits using little extra computing time. Moreover, VFI with Hermite approximation is significantly faster than VFI with Lagrange approximation for the same accuracy, and this advantage increases with the dimension of the continuous states.