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 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