Non-Linear Least Squares

Levernberg-Marquatdt Method

This is a second-order method.

We define an indicator to describe the degree of approximation:


  1. Give an initial value .
  2. For -th iteration, we find an incremental value of, such that the object function reaches a smaller value.
  3. Compute using the above equation.
  4. If , set .
  5. Otherwise, if , set
  6. If is larger than a given threshold, set .
  7. Go back to step 2 if not converged, otherwise return the result.

We use