Manual Page for Command >>> MARQUARDT
Syntax
>>> MARQUARDT: nue
Parent Command
>> CONVERGE
Subcommand

Description
This command sets the Marquardt parameter nue (default: 10.0). During the optimization
process, the Levenberg parameter lambda (see command >>> LEVENBERG) will be divided by
the Marquardt parameter nue after each successful iteration, and it will be multiplied by nue if
the new parameter set leads to an increased value of the objective function, i.e., if an
unsuccessful step was proposed.
A big value for lambda means that a small step along the gradient direction is performed.
A lambda value of zero is equivalent to a GaussNewton step. The former is robust but inefficient, the
latter has a quadratic convergence rate but may lead to unsuccessful steps.
The Marquardt parameter therefore determines how fast the step size and step direction
changes from steepest descent to GaussNewton and vice versa.
Example
> COMPUTATION
>> CONVERGE
>>> maximum number of ITERATIONS: 10
>>> set initial LEVENBERG parameter to: 0.1 to make a
safe first step
>>> MARQUARDT parameter : 2.0 (slow change to GaussNewton steps)
<<<
<<
See Also
>>> LEVENBERG
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Page updated: July 29, 1997