I am trying to accelerate some computations using OpenCL and part of the algorithm consists of inverting a matrix. Is there any open-source library or freely available code to c
I don't have an implementation in Open CL, but both "Numerical Recipes" and Gil Strang's "Into to Applied Math" have wonderful explanations that would be easy to code. "NR" has C code that you could adapt.
calculate the inverse
This is incorrect. You aren't calculating an inverse with LU decomposition, you're decomposing the matrix. If you wanted the inverse, you'd have to do forward back substitution with a series of unit vectors. It's a small but important difference.