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Levenberg-Marquard Algorithm

Figure: Levenberg-Marquardt algorithm for non-linear least square parameter fitting.

The Levenberg-Marquardt method consists of following

steps:

1. Assume initial guesses for the parameter (weight)vectorb.

2. Assign a large value to which means that in the firstiteration the steepest descent method is predominant

and would assure that the method is converging

rapidly towards the lower sum of squared residuals

(Ek).

3. Evaluate the Jacobian matrix J from the equation ofmodel.

4. Use the following equation to obtain the correction toweight w;

w = (JTkJ + I)-1Jk ek

5. Evaluate the new estimate of the weight from thefollowing equation;

wk+1 = wk (JTkJ + I)-1Jk ek

6. Calculate the new value of Ek . If Ek+1 Ek , reduce thevalue ofby a factor of 10 (for example). If Ek+1 > Ek ,

keep old parameters [wk = wk+1] and increase the value

ofby a factor of 10 (eg.).

7. Repeat the steps 3 6 until either (or both) of thefollowing conditions are satisfied:a. Ek does not change appreciably.

b. w becomes very small.