 One common approach of this type, called Weiszfeld's algorithm after the work of Endre Weiszfeld, is a form of iteratively re-weighted least squares.This algorithm defines a set of weights that are inversely proportional to the distances from the current estimate to the sample points, and creates a new estimate that is the weighted average of the sample according to these weights.That is,
This method converges for almost all initial positions, but may fail to converge when one of its estimates falls on one of the given points.