Built-in Mathematica Symbol

FindFit

FindFit[data, expr, pars, vars]
finds numerical values of the parameters pars that make expr give a best fit to data as a function of vars. The data can have the form {{x₁, y₁, ..., f₁}, {x₂, y₂, ..., f₂}, ...}, where the number of coordinates x, y, ... is equal to the number of variables in the list vars. The data can also be of the form {f₁, f₂, ...}, with a single coordinate assumed to take values 1, 2, ....

FindFit[data, {expr, cons}, pars, vars]
finds a best fit subject to the parameter constraints cons.

MORE INFORMATION

FindFit returns a list of replacements for par₁, par₂, ....

The expression expr must yield a numerical value when pars and vars are all numerical.

The expression expr can depend either linearly or nonlinearly on the par_i.

In the linear case, FindFit finds a globally optimal fit.

In the nonlinear case, it finds in general only a locally optimal fit.

FindFit[data, expr, {{par₁, p₁}, {par₂, p₂}, ...}, vars] starts the search for a fit with {par₁->p₁, par₂->p₂, ...}.

FindFit by default finds a least-squares fit.

The option NormFunction->f specifies that the norm f[residual] should be minimized.

The constraints cons can contain equations, inequalities or logical combinations of these.

The following options can be given:

AccuracyGoal	Automatic	the accuracy sought
EvaluationMonitor	None	expression to evaluate whenever expr is evaluated
Gradient	Automatic	the list of gradient components for expr
MaxIterations	Automatic	maximum number of iterations to use
Method	Automatic	method to use
NormFunction	Norm	the norm to minimize
PrecisionGoal	Automatic	the precision sought
StepMonitor	None	expression to evaluate whenever a step is taken
WorkingPrecision	Automatic	the precision used in internal computations

The default settings for AccuracyGoal and PrecisionGoal are WorkingPrecision/2.

The settings for AccuracyGoal and PrecisionGoal specify the number of digits to seek in both the values of the parameters returned, and the value of the NormFunction.

FindFit continues until either of the goals specified by AccuracyGoal or PrecisionGoal is achieved.

Possible settings for Method include "ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "NMinimize" and "QuasiNewton", with the default being Automatic.