One major conclusion that can be drawn from this research is that the recursive structure of the improved algorithm improves run-time exponentially as the level of accuracy is increased. In addition, incorporating parallel processing techniques on the improved algorithm decreases run-time by a factor of about two, on a duo-core machine. We expect that running the algorithm on computers with more cores will further decrease run-time.
You may be asking, so what? How is this algorithm useful?
This algorithm has a multitude of potential uses, although the most prevalent is approximating the solutions to financial systems under stress. The solutions to these systems can only be found by checking individual combinations of variables (represented on the axes of the grid). The algorithm will be useful in quantifying and visualizing these solutions, especially when they are composed with many dimensions. The applications of the algorithms can be extended to other problems in which systems are undergoing stress, such as airports dealing with chain reactions of delays.
The current improvements on the algorithm are not over. There are still some bugs to be worked out, and there are several structural improvements that can be implemented to produce shorter run-times. One of these structural improvements would consist of using convexity in effort to approximate the function in a more intelligent way. Knowing how the approximated function is curved can help achieve the approximation in a shorter time.
You may be asking, so what? How is this algorithm useful?
This algorithm has a multitude of potential uses, although the most prevalent is approximating the solutions to financial systems under stress. The solutions to these systems can only be found by checking individual combinations of variables (represented on the axes of the grid). The algorithm will be useful in quantifying and visualizing these solutions, especially when they are composed with many dimensions. The applications of the algorithms can be extended to other problems in which systems are undergoing stress, such as airports dealing with chain reactions of delays.
The current improvements on the algorithm are not over. There are still some bugs to be worked out, and there are several structural improvements that can be implemented to produce shorter run-times. One of these structural improvements would consist of using convexity in effort to approximate the function in a more intelligent way. Knowing how the approximated function is curved can help achieve the approximation in a shorter time.