Accelerating convergence in the Fermat–Weber location problem

This paper presents a simple procedure for accelerating convergence in a generalized Fermat–Weber problem with I(p) distances. The main idea is to multiply the predetermined step size of the Weiszfeld algorithm by a factor which is a function of the parameter p. The form of this function is derived from the local convergence properties of the iterative sequence. Computational results are obtained which demonstrate that the total number of iterations to meet a given stopping criterion will be reduced substantially by the new step size, with the most dramatic results being observed for values of p close to I.