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Levenberg-Marquardt algorithm

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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. This means that in fact, the method is also a learning method to fit curves to data. 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.

Scientific Area:
MatLab, Python, R


Target Group:

Cite as:
Levenberg, Kenneth (1944). "A Method for the Solution of Certain Non-Linear Problems in Least Squares". Quarterly of Applied Mathematics. 2 (2): 164–168. doi:10.1090/qam/10666.
Marquardt, Donald (1963). "An Algorithm for Least-Squares Estimation of Nonlinear Parameters". SIAM Journal on Applied Mathematics. 11 (2): 431–441. doi:10.1137/0111030. hdl:10338.dmlcz/104299.

Author of the review:
Eligius Hendrix
University of Malaga


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Pablo Guerrero-Garcia

Some remarks on the difference between Levenberg and Marquardt approaches can be found at