We study theoretical and computational aspects of the least squares fit (LSF) of circles and circular arcs. First we discuss the existence and uniqueness of LSF and various parametrization schemes. Then we evaluate several popular circle fitting algorithms and propose a new one that surpasses the existing methods in reliability. We also discuss and compare direct (algebraic) circle fits.

We describe a new method for the fitting of differentiable fuzzy model functions to crisp data. The model functions can be either scalar or multidimensional and need not be linear. The data are n-component vectors. An efficient algorithm is achieved by restricting the fuzzy model functions to sets which depend on a fuzzy parameter vector and assuming that the vector has a conical membership fun...

We consider the problem of fitting a set of points in Euclidean space by an algebraic hypersurface. We assume that points on a true hypersurface, described by a polynomial equation, are corrupted by zero mean independent Gaussian noise, and we estimate the coefficients of the true polynomial equation. The adjusted least squares estimator accounts for the bias present in the ordinary least squar...

During the granulation process of Iron ore sinter mixture, there are many factors affect the granulating effect, such as chemical composition, size distribution, surface feature of particle, and so on. Some researchers use traditional fitting calculation methods like least square method and regression analysis method to predict granulation effects, which exists big error. In order to predict it...