Levenberg–Marquardt algorithm: Difference between revisions

Revision as of 11:43, 11 August 2004

Revision as of 14:30, 11 August 2004

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In [[mathematics]] and [[statistics]], ainimising a sum

Minimising a sum<br>

:<math>S(\vec{x}) = \sum_{i=1}^{m}[f_{i}(\vec{x})]^2</math>,<br>

where <math>f_{i}(\vec{x})</math> represent the components of function <math>\vec{f}</math>, may be solved by the Levenberg-Marquardt algorithm according to<br>

<math>(J^{T}J + \lambda I)\vec{q} = -J^{T}\vec{f}</math>.<br>

where

<math>J</math> represents the Jacobian of the function <math>\vec{f}</math>, <math>\lambda</math> the damping factor, which is altered at every iteration, <math>I</math> the identity, <math>\vec{q}</math> the solution to an iteration step.

:<math>f_{i}(\vec{x})</math>

represent the components of the function

:<math>\vec{f}</math>,

may be solved by the '''Levenberg-Marquardt algorithm''' according to

:<math>(J^{T}J + \lambda I)\vec{q} = -J^{T}\vec{f}</math>.<br>

Here <math>J</math> represents the [[Jacobian]] of the function <math>\vec{f}</math>, <math>\lambda</math> the damping factor, which is altered at every iteration, <math>I</math> the [[identity matrix]], and <math>\vec{q}</math> the solution to an [[iteration]] step.

[[Category:Algorithms]]