Related papers: Least Squares Auto-Tuning
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
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…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…
The least squares method provides the best-fit curve by minimizing the total squares error. In this work, we provide the modified least squares method based on the fractional orthogonal polynomials that belong to the space $M_{n}^{\lambda}…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
The least squares fit to a straight line, when both variables are affected by all equal uncorrelated errors, leads to very simple results for both the estimated parameters and their standard errors, of widespread applicability. In this…
It is shown that whenever the multiplicative normalization of a fitting function is not known, least square fitting by $\chi^2$ minimization can be performed with one parameter less than usual by converting the normalization parameter into…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…
Nowadays, Non-Linear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last years, and this resulted in the development of several open-source…
A numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to…
Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS…
There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…