Weight optimization in HDMR with perturbation expansion method

High dimensional model representation method forms an effective divide-and-conquer method used for the truncated representation of a multivariate function, having N independent variables, in terms of certain number (Formula presented.) of less variate functions. The main aim of this method is not to use all these functions in the representation and to obtain an approximation to the given problem. This results in a need of having a good convergence performance just as it is expected in the other numerical methods. This work aims to increase the convergence rate of HDMR approximation by optimizing the weight function, which appears in the method as Prof. Rabitz suggested first, with the help of the perturbation expansion and fluctuationlessness theory. This work also includes a computational procedure with the help of a testing function to better understand the steps of the proposed method.