An update was released today for No Man's Sky on the PC for both the Steam version and through GOG. The official changelog doesn't seem to be released just yet, but this is what was being tested this past week in the No Man's Sky experimental branch through Steam.
AMD Phenom Support
Thousands of lines of assembly have been rewritten to support AMD CPUs. The game code no longer relies on anything above SSE 2,
Havok Physics has also now created new libs. Game is now confirmed working on Phenom CPUs.

Mouse SmoothingImproved Performance
On CPUs with 4 threads or fewer, performance has been improved.
On CPUs with 8 threads, performance has also been significantly improved.

Radeon 6xxx
Added support for this GPU, which doesn't support OpenGL 4.5 fully.

Player Saves
Help to recover some player saves which had been lost or corrupt.

Alt-Tab has improved
Some systems/configs were crashing or not pausing correctly on Alt Tab. This should now be resolved.

Shader Caching
Framerate was initially stuttering due to shaders not being correctly cached by the GPU on some systems. We have replaced the GPU caching system. You may notice some stutter during the Galactic Map intro to the game (the very first time you run), but it should be smoother from then on (this will be fixed in future). This is particularly true on ATI cards

Max FPS Cap
On some CPU/GPU configurations, setting Max FPS to 60 or 30 was not giving 60 or 30 FPS (causing stuttering). This has been improved.

Intel GPU Detection
We do not currently support Intel GPUS. We are working on this for a future patch, to expand our min spec.
In the meantime, the game will now let you know if you are trying to run with an unsupported GPU. This will hopefully flag for some users that their high end GPU has not been selected.

Gsync has been disabled by default, which was causing an issue for some users

This patch is also reportedly out for the PlayStation 4. Again, a changelog for either platform doesn't seem to exists so the above is the best we have to go on so far. This update also seems to not fix some of the save issues users have reported. It also seems that some users are still crashing as often and, in some cases, more often than before. Some have even reported that this patch prevents them from even launching the game on both platforms.

If you haven't yet, be sure to check out our review for No Man's Sky!