I just need to know what happens to convergencedivergence du

I just need to know what happens to convergence/divergence during the NEWTON RAPHSON method, when you don\'t update the Jacobian Matrix between iterations.

Just a simple, logical, ONE OR TWO SENTENCE response is all I need to confirm my theories. Thanks!

(Below is the question I need my answer for, as a reference.)

Compute the Jacobian for the first iteration, and continue all the iterations without updating it. Does the problem converges? Explain why?

Solution

constant jacobian used for reducing number of computations per iteration at a cost of convergence.

It may or may not converge, and it totally depends upon shape of multi dimention equation.

1. jacobian is the slope of the multidimention equation in all dimentions. It is safe to update jacobian(slope for next iteration) inorder to track the curve to words its minimum point.

2. in case of constant jacobian slops won\'t update , slope of every iteration is same. if multidimension curve has so many ups and downs, then actual slope of next iteration is very far from constant jacobian. hance we track minimum point in wrong direction.

available! for doubts. :)