Resolution approximation method; An analysis, failures and successes

Abstract

The resolution approximation method is introduced for the first time for data approximating with minimizing an energy function. The minimization problem of the corresponding energy function is analyzed with three different distances, maximum distance, average distance and Ecleadian distance. Interestingly, the first approximations for monomials with introduced distances are equivalent to descriptive statistics such as minimum, maximum, average and median. Unfortunately, the resolution approximation methods with monomials fail. A cure with Haar scale functions is introduced. The theoretical results are validated with some examples. MSC Classification: 41A05 , 94A16