Describes a powerful optimization algorithm which iteratively solves a weighted least squares approximation problem in order to solve an L_p approximation problem. 1 Approximation Methods of approximating one function by another or of approximating measured data by the output of a mathematical or computer model are extraordinarily useful and ubiquitous. In this note, we present a very powerful ...

Many biological and astronomical forms can be best represented by ellipses. While some more complex curves might represent the shape more accurately, ellipses have the advantage that they are easily parameterised and define the location, orientation and dimensions of the data more clearly. In this paper, we present a method of direct least-squares ellipse fitting by solving a generalised eigens...

This is the usual introduction to least squares fit by a line when the data represents measurements where the y–component is assumed to be functionally dependent on the x–component. Given a set of samples {(xi, yi)}i=1, determine A and B so that the line y = Ax + B best fits the samples in the sense that the sum of the squared errors between the yi and the line values Axi + B is minimized. Note...