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Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters of the model curve (,) so that the sum of the squares of the deviations () is minimized:
FEATool Multiphysics is a Matlab GUI toolbox for finite element FEM and PDE multiphysics simulations. FEniCS Project is a collection of project for automated solutions to PDEs. Hermes is a C++ library of advanced adaptive finite element algorithms to solve PDEs and multiphysics coupled problems. Fityk is a curve fitting and data-analysis ...
Origin is a proprietary computer program for interactive scientific graphing and data analysis. It is produced by OriginLab Corporation, and runs on Microsoft Windows. It has inspired several platform-independent open-source clones and alternatives like LabPlot and SciDAVis. Graphing support in Origin includes various 2D/3D plot types.
The program can produce generalizations of the normal, logistic, and other distributions by transforming the data using an exponent that is optimized to obtain the best fit. This feature is not common in other distribution-fitting software which normally include only a logarithmic transformation of data obtaining distributions like the ...
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. In regression analysis, least squares is a parameter estimation method based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each ...
TableCurve 2D is a linear and non-linear Curve fitting software package for engineers and scientists that automates the curve fitting process and in a single processing step instantly fits and ranks 3,600+ built-in frequently encountered equations enabling users to easily find the ideal model to their 2D data within seconds.
Consider a set of data points, (,), (,), …, (,), and a curve (model function) ^ = (,), that in addition to the variable also depends on parameters, = (,, …,), with . It is desired to find the vector of parameters such that the curve fits best the given data in the least squares sense, that is, the sum of squares = = is minimized, where the residuals (in-sample prediction errors) r i are ...