[math] interface for UnivariateRealFunction (differentiability)

[Matt Cliff <ma...@mattcliff.com>]

What is the purpose for having the firstDerivative() and 
secondDerivative() methods on a UnivariateRealFunction ?

   It is a little troubling to me to have at this level (perhaps if needed 
a subclass such as UnivariateDifferentiableRealFunction ).  Most numerical 
processes only require a function analysis, also when doing anything 
'challenging'  the differentiablity can get complicated, if not 
impossible.

  

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      Matt Cliff            
      Cliff Consulting
      303.757.4912
      720.280.6324 (c)


      The label said install Windows 98 or better so I installed Linux.


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Re: [math] interface for UnivariateRealFunction (differentiability)

["J.Pietschmann" <j3...@yahoo.de>]

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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