Stochastic approximation—A powerful method for solving deterministic numerical problems

AbstractThe stochastic approximation method of Robbins and Monro, after some modifications, is shown to be a powerful technique for obtaining numerical solutions of deterministic problems. Both algebraic equations and two point boundary value problems in ordinary differential equations are solved. The convergence rate is shown to be reasonably fast and results are surprisingly accurate. Our proposed procedure is more general than the original approach. Deterministic problems with multiple roots can be solved whereas the original Robbins-Monro method is restricted to a monotone increasing regression function with a single root