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.
Cai and Judd gratefully acknowledge NSF support (SES-0951576). The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Mathematical Methods of Operations Research June 2015, Volume 81, Issue 3, pp 245-267 Date: 13 Feb 2015 Dynamic programming with Hermite approximation Yongyang Cai, Kenneth L. Judd citation courtesy of