The current algorithm is structured to reduce time, although it does require more testing and debugging. Essentially the algorithm starts with a sparse grid, and determines the upper and lower bounds of the approximated function. Then, each lower bound is paired with the nearest diagonal upper bound to define a set of regions. Each of these regions is then analyzed simultaneously, via MATLAB's parallel processing capabilities. This process improves the accuracy of the grid search approximation by decreasing the diagonal distance between the upper and lower bounds. The process is repeated, recursively, until the desired accuracy is obtained.
An example of this process is shown below:
An example of this process is shown below: