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From "J.Pietschmann" <j3322...@yahoo.de>
Subject Re: [math] interface for UnivariateRealFunction (differentiability)
Date Fri, 07 Nov 2003 22:01:21 GMT
Matt Cliff wrote:
> What is the purpose for having the firstDerivative() and 
> secondDerivative() methods on a UnivariateRealFunction ?
> 
The first derivative could be used in a Newton solver. The
second derivative could be used in yet another higher order
root finder, or for providing error estimates and guidance
in modified, more robust Newton root finders (sorry, I'm
too lazy to look up method names).

The reason they are in the function class is that partial
results might be shared for calculating the values of the
function and its derivatives. Reusing intermediate results
can bring Newton in front of the Brent-Dekker solver in
terms of efficiency again.

J.Pietschmann



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