Daily Archives: January 28, 2008

Levenberg-Marquardt algorithm


In mathematics and computing, the Levenberg-Marquardt algorithm (or LMA) provides a numerical solution to the problem of minimizing a function, generally nonlinear, over a space of parameters of the function. These minimization problems arise especially in least squares curve fitting and nonlinear programming.
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. On the other hand, for well-behaved functions and reasonable starting parameters, the LMA tends to be a bit slower than the GNA.
The LMA is a very popular curve-fitting algorithm; most software with generic curve-fitting capabilities provides an implementation of it.