What is the difference between the Dishonest Newton method and the Very Dishonest Newton method? Is there a difference or do they mean the same thing?

I have tried searching for this on the internet but I can't find anything. I understand that in the ordinary ("honest") Newton method, the Jacobian is computed in each iteration. If we reuse the same Jacobian for several iterations, this is referred to as the Dishonest Newton method (DN) by some sources and as the Very Dishonest Newton method (VDN) by others.

Intuitively, I would think that the Very Dishonest Newton method reuses the same Jacobian for more iterations than Dishonest Newton. Maybe in VDN the Jacobian is only computed once? But I have not been able to verify this.

I would prefer some credible sources with clear descriptions of both methods as I want to refer to them in my master's thesis.

  • 2
    $\begingroup$ it's got to do with how often you update your Jacobian. if your Jacobian stays the same throughout the Newton iteration, then you're being very dishonest. If you update it, say, every $K$th iteration (with $K>1$) then one can say your method is just dishonest. :) $\endgroup$ – GoHokies Sep 14 '18 at 6:53
  • 5
    $\begingroup$ oh, and because you shouldn't trust strangers on the internet (they may range from somewhat to very dishonest), here's an honest reference from the folks at UIUC that backs up my statement: link $\endgroup$ – GoHokies Sep 14 '18 at 6:56
  • 1
    $\begingroup$ and another reference: Crow, Computational Methods for Electric Power Systems, 3rd ed., p. 74-75 $\endgroup$ – GoHokies Sep 14 '18 at 7:02
  • 1
    $\begingroup$ @GoHokies Thanks! The book by Crow was a great reference. I think your comments qualify as an answer. $\endgroup$ – Pirkiz Sep 14 '18 at 8:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.