Re: [boost] Numerical Quadrature Library/Boost.Accumulators

From: Matthias Schabel (boost_at_[hidden])
Date: 2006-12-07 17:01:02

>> As far as I can see, precision needs to be the same type as the
>> return type since it represents
>> uncertainty in the latter. That is, the range of possible return
>> values would be [result - n*error,
>> result + n*error]. Do you have a case in mind where this isn't true?
>
> This is always true when you can define such an interval, which is
> not the case for an integral of a complex valued function ( no "<" on
> complex) .

I'm certainly not an expert in the numerical analysis involved in  
convergence of complex
functions, but I imagine that this is essentially a subset of the  
more general case of
vector-valued functions. For the latter case, the first-order  
assumption is that error variances
are uncorrelated, leading to a diagonal covariance matrix between  
components. In this
way, if a complex error was returned, it would indicate a gaussian  
distributed set of errors
in the real and complex components forming an ellipse oriented with  
the real and imaginary
axes. Naturally, covariances are important in many cases, but also  
are more heavyweight.
I suppose that a N-dimensional result class could return an N- 
dimensional value and an
NxN covariance matrix that reduced to diagonal in the case where  
covariances are negligible...

Matthias

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Matthias Schabel, Ph.D.
Assistant Professor, Department of Radiology
Utah Center for Advanced Imaging Research
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