A note on the choice weighting functions in the method of moments

The objective is to show from a mathematical standpoint that there are certain rules that must be followed in the choice of weighting functions used in the method of moments (MM). It is shown that for a particular problem it is the operator that dictates the method (Galerkin´s method or another method such as the method of least squares) to be applied, and it is not computational considerations only. For example, it is shown that in solving Hallen´s and Pocklington´s equation by the method of moments, it is unnatural to choose the weighting functions which are zero at the ends of the domain of the solution. The deficiency of certain weighting functions is presented based on mathematical reasoning, and a numerical example is given to illustrate the effect of the choice of the weighting functions on the rate of the convergence of the solution.