# Matrix inversion of an analytical function

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.

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Probably this question is more suitable on scicomp.stackexchange – Shuhao Cao Jul 10 '12 at 16:02

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.