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Max-plus based methods have been recently explored for solution of first-order Hamilton-Jacobi-Bellman equations by several authors. In particular, McEneaney's curse-of-dimensionality free method applies to the equations where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms. In previous works of McEneaney and Kluberg, the approximation error of the method was shown to be O(1/(N&#x03C4;))+O(&#x221A;&#x03C4;) where &#x03C4; is the time discretization step and N is the number of iterations. Here we use a recently established contraction result of the indefinite Riccati flow in Thompson's metric to show that under different technical assumptions, still covering an important class of problems, the total error incorporating a pruning procedure of error order &#x03C4;2 is O(e-&#x03B1;N&#x03C4;)+O(&#x03C4;) for some &#x03B1; &gt; 0 related to the contraction rate of the indefinite Riccati flow.

Contraction of Riccati flows applied to the convergence analysis of the max-plus curse of dimensionality free method