The minimization condition can be converted into the problem of
solving a nonlinear system by requiring that the derivative with
respect to each of the parameters must vanish. We have

(39) |

We can try to solve this nonlinear system by using Newton's method. This method starts with a trial value for the parameter vector and then seeks the vector change that improves the trial value. Thus we seek the solution to

(40) |

where

(42) |

Actually this linear system is the same as what we had to solve for the linear least squares problem. The connection can be made more explicit by realizing that a Taylor's expansion of in small shifts about the vector is just

(44) |

The error in the th fitted parameter is
found from the diagonal element of the matrix at the minimum of .