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From: garcia@maze.ruca.ua.ac.be (Johan Garcia)
Subject: HELP : Non-linear System of equations
Message-ID: <1994Dec7.174332.28295@reks.uia.ac.be>
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Date: Wed, 7 Dec 1994 17:43:32 GMT
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Antwerpen Dec 7th 1994

Dear Sir,

During one year I have tried to avoid solving a certain system of equations
that appear in my job. Unfortunately enough any other approximation that I
tried does not lead to a good solution of my problem and I will have to face
the solution of the problem given bellow:

It is needed to find lamb(i,k) such that:

 Sum in i of ( (n(i,j,k) + 1)/(lamb(i,k) + lamb(j,k))) = f(j,k)
 Sum in j of ( (n(i,j,k) + 1)/(lamb(i,k) + lamb(j,k))) = f(i,k)

 The constraints in i, j, k, f(i,k) and n(i,j,k) are such that:

 i varies from 0 until M_1
 j varies from 0 until M_1
 k varies from 0 until M_2
 sum in i and k of (f(i,k)) = M_3

 M_1, M_2 M_3 are all natural positive
 f(i,k) is limited positive and real
 f(i,k) is different from zero for any pair i,k
  

I suppose such a problem must have been already faced and so there must
be already an algorithm to solve it.
I would appreciate very much if some one could help me on it.
Thank you very much for your help.

My e_mail is : garcia@ruca.ua.ac.be

Johan

University of Antwerpen
