Dynamic Programming with Hermite Approximation

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