3
$\begingroup$

Following problem:

I have a function

$f(x_1,x_2)$

and Im looking for the inverse $finv(x_1,x_2)$ of the function which is defined through:

$\int f(x_1,y)\cdot finv(y,x_2) d y =\delta(x_1,x_2) $

where $\delta(x_1,x_2) $ is the Dirac delta function.

When I'm trying to discretize $f$ and then to invert as usual matrix I get numerically bad results. I mean the result is ok, but I need extremely fine discretization.

I'm sure there should be some other method than the poor man inversion. Something like inversion with weights or similar.

Probably there exist already a c++ library for such problem.

$\endgroup$
  • $\begingroup$ Probably this question is more suitable on scicomp.stackexchange $\endgroup$ – Shuhao Cao Jul 10 '12 at 16:02
1
$\begingroup$

In case your $f$ is a function only of $x_1-x_2$ and limits of integration are $-\infty$ to $+\infty $ then a solution via Fourier transform method can be found on Wikipedia.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.