Functional approximations and dynamic programming

This paper indicates some ways in which the theory of approximation can be used to increase the range of present day computers. Although the primary interest is in applying these techniques to the functional equations occurring in the theory of dynamic programming. These same methods are applicable, and even more readily, to the classical functional equations of mathematical physics. The objective of the paper is to trade additional computing time, which is expensive, for additional memory capacity, which does not exist.