@smartnose - this maybe what you are looking for. http://support.amd.com/en-us/kb-articles/Pages/AMD-Radeon-GPU-PRO-Linux-Beta-Driver–Release-Notes.aspx
Please read the instructions several times before attempting to add this driver. When it is installed you NOT be able to see it via software and updates, additional drivers.
If you are uncertain of anything stay on your current version of Ubuntu Mate.
I started with a “CLEAN” install of Mate 15.04- there is an option when installing Mate. Then insure all updates are done.
I then updated to 16.04, rebooted and then installed the AMD Driver, this seemed to work ok for me, however please note the Kernel has moved forward since the release. Ubuntu Users forum also has a good step by step guide and I would follow this rather than AMDs documentation.
Good luck and as wolfman said above USE AT YOUR OWN RISK