How to run linux on PS3?
As matters currently stand, there is no "safe" way to use Linux on a PS3 you buy brand new from a retail store. Since the firmware will not provide you low level access to the hypervisor, it's impossible to install Linux without first replacing the firmware. The console will only install firmware with Sony's cryptographic signature, and you are not allowed to downgrade the firmware; it is not possible to overwrite the firmware unless you can build your own and forge Sony's signing key.
To directly answer your questions:
Are there ways? Yes, because Sony is not very good at keeping their signing keys a secret. You will need to do research on custom firmware. Using such firmware would void your warranty, and you risk having your console banned from the Playstation Network if you connect to it and Sony detects that you're not running an official firmware release. Even if a firmware is "safe" one day, it might not be the next.
Would you be able to run Linux on one that you bought? "Maybe." Do your research, and pay very close attention to any commentary about whether or not the hacks work with newer hardware revisions. Do not buy unless you're sure that the hack you intend to use will work with that console, proceeding recklessly could permanently damage your purchase.
Instructions that are more specific than this are unlikely to be posted as answers, because nobody wants Sony breathing down their neck.
I agree with others. Performance on a single PS3 isn't going to be close to what you would get with a white box (DIY) PC w/ any recent NVIDIA GPU plus CUDA for those cases where you need it.
Neither the PS3 running Linux or your own x64 box will be massively cool just because. CUDA helps with numerical computations, so if you are a heavy user of software like R, Octave, etc. you will enjoy significant improvement (I have heard that R runs 7x faster w/ CUDA based libraries substituted for the default).
Don't expect to suddenly see Firefox or libreOffice running at the speed of thought. Software performance is not just based on the number of cores or specialized processors--it has to be written to take advantage of them. I.e. just sticking a fast NVIDIA card in your PC isn't going to make R crunch your numbers faster. It is only because there are CUDA specific libraries (e.g. BLAS) which you can use when you build R--likely from source, unless someone has already created an RPM (or DEB, etc.) with these libraries. Not too hard, but you need to have the software which knows how to leverage the hardware to see the specialized increase in performance.
That said, I am pretty pissed that Sony dicked PS3 owners over by blocking this functionality. While it wouldn't be a super computer, being able to get double duty out of my PS3 would have been cool. As mentioned, the limited RAM makes desktop use less than optimal.
PS3s, when they are properly networked, have been used to create some amazing super computer clusters using standard Linux clustering software. When this is done the limited RAM isn't a problem, and they are usually custom programmed for things the platform is really good at, like figuring out protein folding.
If you are just interested in the power of distributed computing, there is a BOINC client for PS3 which you can install from PlayStation Network where you can donate your PS3's power, typically to some academic group working on difficult bioinformatics or statistical problems (e.g. data mining the human genome). You just run it like a screen saver when you are not playing.
It is pretty clear that Sony doesn't give a rats ass for either the use of the PS3 as nodes in clusters or letting users use it as a Linux PC. If they had a soul (or brain?) they would figure out how to let users expand the RAM and charge them to download and install some custom Linux w/ a decent repo of cool things prebuilt. Not a huge market, but you can certainly see the advantage of having something which could be used for school work and gaming, esp. if you are in charge of marketing to kids who have to come up with good arguments why they need a PS4. ;)