Related papers: Data boundary fitting using a generalised least-sq…
Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the chi^2 hypersurface, depending on a set of parameters {P_i}. This is usually done using the Levenberg-Marquardt algorithm. The main…
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…
An important problem in applications is the approximation of a function $f$ from a finite set of randomly scattered data $f(x_j)$. A common and powerful approach is to construct a trigonometric least squares approximation based on the set…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
In this article, we describe a function fitting method that has potential applications in machine learning and also prove relevant theorems. The described function fitting method is a convex minimization problem and can be solved using a…
Minimization of boundary curvature is a classic regularization technique for image segmentation in the presence of noisy image data. Techniques for minimizing curvature have historically been derived from descent methods which could be…
The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment…
This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding…
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…
Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M-1)-dimensional topological…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
I consider the task of experimental data fitting. Unlike the traditional approach I do not try to minimize any functional based on available experimental information, instead the minimization problem is replaced with constraint satisfaction…
We address the problem of epipolar geometry using the motion of silhouettes. Such methods match epipolar lines or frontier points across views, which are then used as the set of putative correspondences. We introduce an approach that…
Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares problem arises naturally…