What is the most efficient way to solve system of equations containing the digamma function?

Posted by Neil G on Stack Overflow See other posts from Stack Overflow or by Neil G
Published on 2010-04-11T03:16:19Z Indexed on 2010/04/11 4:43 UTC
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equation-solving

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gsl

What is the most efficient way to solve system of equations involving the digamma function?

I have a vector v and I want to solve for a vector w such that for all i:

digamma(sum(w)) - digamma(w_i) = v_i

and

w_i > 0

I found the gsl function gsl_sf_psi, which is the digamma function (calculated using some kind of series.) Is there an identity I can use to reduce the equations? Is my best bet to use a solver? I am using C++0x; which solver is easiest to use and fast?

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