From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: Help please ! A kind of inverse problem
Date: 31 Jan 2000 12:40:15 GMT
Newsgroups: sci.math.num-analysis
Summary: [missing]

In article <388F3547.A666A690@utc.fr>,
 Yacine Benabderrahmane <Yacine.Benabderrahmane@utc.fr> writes:
|> Hi there, hope there will be someone helping me for this,
|> 
|> I want to find the function a(x) that satisfies :
|> 
|> C=int( a(x)*K(x) dx ) , x=0..A
|> 
|> where C and A are known constants and the function K(x) is known.
|> 
|> If there is no analytical solution, what is the best way to solve this
|> problem numerically?
impossible job. 
how will you specify a function on an interval by giving just one number of
information for it? every function b(x) with 
   int( b(x)*K(x) dx) =0 
added to your hypothetic a would give the same C, and there is a whole space of 
functions b which do that. I guess you have something in mind like

    C(y) = int_0^A ( a(x)*K(x,y) dx),  0<=y<=A 
a so called Fredholm integral equation of the first kind, a not well posed
inverse problem, which must be solved numerically using so called regularization
techniques.  you must take a look in some advanced numerical analysis text to 
read about that, e.g. Bakers text "the numerical treatment of integral
equations", oxford university press 1977.
hope this helps
peter