Least fourth powers: optimisation method favouring outliers

摘要

A new optimisation method is proposed in this paper. The least fourth powers method allows fitting a geometric figure to a set of points in such a way, that the maximal value of displacement between the fitted figure and the points is smaller than in the least squares method. This property can be very useful in some engineering tasks, e.g. in the realignment of a railway track. The objective function of the new optimisation method is proposed, along with an analysis of some theoretical properties of the new method. It was pointed out that some computational problems can appear. Appropriate computational techniques were proposed to overcome these problems. Detailed algorithms were presented and illustrated by numerical examples. The efficiency of various computational techniques is compared, and the resulting conclusions are presented.