A decomposition scheme for the Hamilton-Jacobi equation
One way to compute optimal control in completely observable stochastic optimal control problems is to solve the Hamilton-Jacobi Equation. We propose to replace in the quasi linearization technique of Bellman [1] the step of inversion of a linear system of dimension n by several steps of n linear equations of dimension 1 in parallel or in sequence. We are then led to apply for instance splitting up methods-studied in particular in [3], [6], [8], [9]. We obtain what we call a decomposition scheme to approximate evolutive Hamilton-Jacobi Equation. We study convergence results as time steps converge to zero with compacity methods adapted from [4] and give some numerical results.
The present invention provides a process for the preparation of an enriched carboxylic acid compositions produced by the method of composition of the carboxylic acid is included in contact with the enrichment feed in the enrichment zone. The present invention is then to remove the catalyst from the carboxylic acid composition to a method and that the resulting composition for the preparation of a catalyst removal composition.