This paper analyses the implementation of the generalizedfinite differences method for the HJB equation of stochastic control, introduced by two of the authors in [Bonnans and Zidani,SIAM J. Numer. Anal.41 (2003) 1008–1021]. The computation of coefficients needs tosolve at each point of the grid (and for each control)a linear programming problem.We show here that, for two dimensional problems, this linear programming problem can be solved in O(p max) operations, where p max is the size of the stencil. The method is based on a walk on the Stern-Brocot tree,and on the related filling of the set of positive semidefinite matrices of size two.
