Short answer: AFAICT there isn’t even a not-simple solution.
To use a GPU effectively for dense eigensystem computations is quite difficult. The functionality was only recently added to the CUDA libraries (useless to you) and is conspicuously absent from the prominent projects using OpenCL (e.g. ArrayFire). There was some work in the clMagma project, but that seems to have been abandoned well before recent upgrades to the AMD software stack.
You say “decomposition”, so I assume you mean for dense matrices. For a few eigenvalues/vectors of sparse matrices there is more hope, but it’s still not simple.