To directly answer the question: no. It is not possible to install a Linux on your PS3 without using an external computer. As already noted, last year Sony did an about-face on installs of Linux, removing the capability for native installs from the PS3 Slim. Earlier this year Sony began issuing requiring firmware updates that disabled the ability to install a Linux on the older Fat Playstation 3. There are various firmware hacks that will still allow you to install a Linux on both the PS3 Slim and the original PS3. You just wouldn't want to unless you plan on running a pure console interface, or want to use a PS3 as a server.
Running Linux on PS3 from USB? Discussion in 'Other OS (Linux)' started by SockNastez, Dec 27, 2016. I install Linux on a USB key or external hdd. How to Turn Your PlayStation 3 Into a Linux PC. Which allows the PS3 to install Ubuntu. When you restart the PS3, plug a mouse and keyboard into the USB ports.
In either case, you could build an x86 computer that would be much more power efficient, and performance efficient, for those tasks. The catastrophically big problem with Linux on the Playstation 3 is, not unsurprisingly, Nvidia. Nvidia outright refuses to produce a PowerPC compiled Nvidia-GLX driver, which excludes the possibility of any RSX support.
This means that the only graphics driver the Playstation 3 will use under PowerPC Linux. So, if you had asperations to install a Linux on the PS3 for purposes of watching videos, playing emulated games, or so on, well, here's a little expirement for you. Download Mepis Linux, and tell it to start up in VESA mode from the LiveCD. Now go ahead, browse the web. Play some music. Do the stuff that you would normally do.
The Playstation 3, under Yellow Dog, Debian, or Suse Linux. This is one of the reasons Sony's termination of Linux support really wasn't a big deal. The desktop end-user experience was a horrid mess, and you were stuck with extremely light-weight window managers to fit into the Playstation3's anemic memory profile. The Playstation 3 was only useful to a *nix user for the purposes of either running as a server, or running as a pure number-crunching machine, say for distributed tasks like.