This is a research planning grant to investigate a method for determining the parameters of model functions. This method may prove to be less sensitive to noise and more generally applicable than commonly used methods such as least-squares (LS) and its variations. The algorithm for this method consists of multiplying the original model function by a set of "test functions" and then integrating to form the inner products. The data points are multiplied by the same test functions and numerically integrated. The two results are set equal to one another, yielding a system of constraints on the unknown parameters. For sufficiently many test functions, this system of constraints can be solved for the unknown parameters. During the planning period it will be determined whether this method is feasible as an alternative to other modeling techniques. In particular, it may be useful when measurement errors are not known or there are possible outliers that one does not wish to delete. The method will be applied to a variety of data sets, and well-conditioned test functions will be examined to improve its performance.
