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Design Languages >> Verilog-AMS >> Third derivative
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Message started by Nano_Model on Aug 4^th, 2007, 11:23am

Title: Third derivative
Post by Nano_Model on Aug 4^th, 2007, 11:23am

For Newton's method to work, the third derivative of a device I-V has to exist. Is that true? Why's that?

Title: Re: Third derivative
Post by Geoffrey_Coram on Aug 6^th, 2007, 6:21am

What do you mean by "work"?

It may be that the proof of global convergence of Newton's method requires a third derivative. However, I'm sure that many circuit simulators converge fine even when some of the functions don't even have second derivatives. They're not using strict Newton-Raphson (there's some damping of the steps), and they're not guaranteed to converge -- they just "usually" do.

Title: Re: Third derivative
Post by Visjnoe on Aug 13^th, 2007, 12:04pm

Dear Nano_Model,

given a good intial guess, the convergence criterium for Newton-Raphson is:

Code:

|f(x)f"(x)|<[f`(x)]^2

So there's no third derivative involved.

Regards

Peter

Title: Re: Third derivative
Post by Nano_Model on Aug 14^th, 2007, 5:16pm

:-? oh really.

Now I have another very basic question. Why is Newton Raphson method "dominates" circuit simulation methods?

Title: Re: Third derivative
Post by Visjnoe on Aug 15^th, 2007, 12:04am

Dear Nano_Model,

I cannot help you with this one. I just know it is a classic numerical method to solve a set of nonlinear algebraic equations. If you have other (better) numerical methods, you can build your own simulator I guess :)

Regards

Peter

Title: Re: Third derivative
Post by Nano_Model on Aug 20^th, 2007, 2:28pm

Hi Peter....thanks I hope I "will" come up with such a better method .... ;D