Nonlinear Minimization That Works!

• Some solutions to this problem are

• 1) Conjugate Gradient, but note matrix no longer sparse and so iterative approach not so natural.

• 2) Marquardt's method changes A in ad-hoc fashion, solving (NL.1) with the replaced value

  

  where Q is Marquardt's Parameter

  

• Suppose, . Then shifts are unchanged for large , small for small .

• Increase Q if increases when you use (NL.1).

• Decrease Q if decreases when you use (NL.1).