Dynamic programming with shape-preserving rational spline Hermite interpolation

Numerical methods for dynamic programming often use value function iteration and interpolation. We present a novel shape-preserving rational spline approximation method that improves value function iteration in terms of both stability and accuracy compared to more common methods.

► Dynamic programming methods require good approximation methods. ► Standard methods include piecewise linear or polynomial approximations. ► Standard methods ignore shape properties. ► We introduce a Hermite interpolation with shape preservation. ► This method is reliable and efficient when used in value function iteration.