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In [[mathematics]] and computing, the '''Levenberg–Marquardt algorithm (LMA)''',
The algorithm was first published by Kenneth Levenberg, while working at the [[Frankford Arsenal|Frankford Army Arsenal]]. It was rediscovered by [[Donald Marquardt]] who worked as a [[statistician]] at [[DuPont]] and independently by Girard, Wynn and Morrison.</ref> 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]].▼
The LMA is used in many software applications for solving generic curve-fitting problems. However, as for many fitting algorithms, the LMA finds only a [[local minimum]], which is not necessarily the [[global minimum]]. The LMA interpolates between the [[Gauss–Newton algorithm]] (GNA) and the method of [[gradient descent]]. The LMA is more [[Robustness (computer science)|robust]] than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be a bit slower than the GNA. LMA can also be viewed as Gauss–Newton using a [[trust region]] approach.
▲The algorithm was first published in 1944 by Kenneth Levenberg, while working at the [[Frankford Arsenal|Frankford Army Arsenal]]. It was rediscovered in 1963 by [[Donald Marquardt]] who worked as a [[statistician]] at [[DuPont]] and independently by Girard, Wynn and Morrison.
== The problem ==
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