The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

In this note we suggest a new iterative least squares method for estimating scalar and vector ARMA models. A Monte Carlo study shows that the method has better small sample properties than existing least squares methods and compares favourably with maximum likelihood estimation as well.

This report contributes to the solution of non-negative least squares problem (NLS). The NLS problem is a substantial part of a learning procedure of associative networks. First, stopping conditions suitable for iterative numerical algorithms solving the NLS problem are derived. The conditions allow to control the solution found in terms of optimized objective function. Second, a novel sequenti...

Given a dense set of points lying on or near an embedded submanifold M0 ⊂ Rn of Euclidean space, the manifold fitting problem is to find an embedding F :M → Rn that approximatesM0 in the sense of least squares. When the dataset is modeled by a probability distribution, the fitting problem reduces to that of finding an embedding that minimizes Ed[F], the expected square of the distance from a po...

Along with the science research field is more and more wide, solve large-scale over determined system of linear equations has become an important problem , and the parallel processing technology also become the trend of the research. Firstly, this paper introduces the basic principle of the curve fitting least squares serial algorithm, based on the least square principle we found an parallel le...

Image registration has many real life applications. Affine image registration is one of the commonly-used parametric models. Iterative solution methods for the underlying least squares problem suffer from convergence problems whenever good initial guesses are not available. Variational models are non-parametric deformable models that have been proposed based on least squares fitting and regular...

We present a method to reconstruct a surface from a group of points, each provided with two parameters. The kind of reconstructed surface can be a Bezier surface, a B-spline surface or any surface generated by a basis of functions. The usual method involved in such a reconstruction is the least squares approach. Our original fitting method called LP-fitting uses a linear program for minimizing ...

People employ the function-on-function regression to model relationship between two stochastic processes. Fitting this model, widely used strategies include functional partial least squares algorithms which typically require iterative eigen-decomposition. Here we introduce a route of based upon Krylov subspace. Our can be expressed in forms equivalent each other exact arithmetic: One is non-ite...