Nonlinear Least Squares Optimization Task
Jump to navigation
Jump to search
A Nonlinear Least Squares Optimization Task is a Least Squares Optimization Task that can fit a set of m observations with a model that is non-linear in n unknown parameters (m > n).
- AKA: Nonlinear Least Squares Regression Task, NonLinear Least Squares Estimation Task, Nonlinear Least Squares Task.
- Context:
- It can be solved by a Nonlinear Least Squares Optimization System (that implements a nonlinear least squares optimization algorithm).
- …
- Counter-Example(s):
- See: Nonlinear Regression, Kernel Regression.
References
2017
- (ESH,2017) ⇒ Engineering Statistics Handbook "Nonlinear Least Squares Regression" http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd142.htm Retrieved 2017-08-13
- QUOTE: Extension of Linear Least Squares Regression - Nonlinear least squares regression extends linear least squares regression for use with a much larger and more general class of functions. Almost any function that can be written in closed form can be incorporated in a nonlinear regression model. Unlike linear regression, there are very few limitations on the way parameters can be used in the functional part of a nonlinear regression model. The way in which the unknown parameters in the function are estimated, however, is conceptually the same as it is in linear least squares regression.
Definition of a Nonlinear Regression Model - As the name suggests, a nonlinear model is any model of the basic form,
[math]\displaystyle{ y=f(x ;\beta )+\varepsilon }[/math],
in which
- 1. the functional part of the model is not linear with respect to the unknown parameters, [math]\displaystyle{ \beta_0,\beta_1,…, }[/math] and
- 2.the method of least squares is used to estimate the values of the unknown parameters.
- QUOTE: Extension of Linear Least Squares Regression - Nonlinear least squares regression extends linear least squares regression for use with a much larger and more general class of functions. Almost any function that can be written in closed form can be incorporated in a nonlinear regression model. Unlike linear regression, there are very few limitations on the way parameters can be used in the functional part of a nonlinear regression model. The way in which the unknown parameters in the function are estimated, however, is conceptually the same as it is in linear least squares regression.
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/non-linear_least_squares Retrieved:2014-6-28.
- 'Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m > n). It is used in some forms of non-linear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences.