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
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the r ...
curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data i ...
. The LMA interpolates between the
Gauss–Newton algorithm (GNA) and the method of
gradient descent. The LMA is more
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 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 Army Arsenal. It was rediscovered in 1963 by
Donald Marquardt Donald W. Marquardt (March 13, 1929, New York City – July 5, 1997, New Castle, Delaware) was an American statistician, the rediscoverer of the Levenberg–Marquardt nonlinear least squares fitting algorithm.Paul Davis (1993)Levenberg–Marquart ...
,
who worked as a
statistician
A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors.
It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...
at
DuPont, and independently by Girard,