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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 nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations.
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting .
Another method involves the use of branch and bound techniques, where the program is divided into subclasses to be solved with convex (minimization problem) or linear approximations that form a lower bound on the overall cost within the subdivision. With subsequent divisions, at some point an actual solution will be obtained whose cost is equal ...
Non-linear least squares problems arise, for instance, in non-linear regression, where parameters in a model are sought such that the model is in good agreement with available observations. The method is named after the mathematicians Carl Friedrich Gauss and Isaac Newton , and first appeared in Gauss's 1809 work Theoria motus corporum ...
Powell's dog leg method, also called Powell's hybrid method, is an iterative optimisation algorithm for the solution of non-linear least squares problems, introduced in 1970 by Michael J. D. Powell. [1] Similarly to the Levenberg–Marquardt algorithm, it combines the Gauss–Newton algorithm with gradient descent, but it uses an explicit trust ...
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 ...
Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting solution. RLS is used for two main reasons. The first comes up when the number of variables in the linear system exceeds the number of observations.
The lattice recursive least squares adaptive filter is related to the standard RLS except that it requires fewer arithmetic operations (order N). [4] It offers additional advantages over conventional LMS algorithms such as faster convergence rates, modular structure, and insensitivity to variations in eigenvalue spread of the input correlation ...