Currently Sony is rushing to plug any holes that would allow you to install a guest OS on a PS3, so while you may find a hack that will allow you to install a guest OS, that whole may be quickly plugged.

If you are fortunate enough to still have the capability to install a guest Os you will want to use yellowdog http://www.yellowdoglinux.com/support/installation/ which does not require a computer for installation. You only need a computer to download and burn the installation DVD.

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. 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... is VESA.

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. http://www.mepis.org/mirrors

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... IS SLOWER.

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 Folding@Home.

Problem is, the PS3 already does Folding@Home in the Sony firmware. The native firmware also has accelerated graphics support. The native firmware has media playback. Okay, fine. The native firmware doesn't do Ogg Vorbis, Ogg Theora, or WebM. The list of supported media formats is pathetically low, and the playlist capabilities rival those of a Sega Saturn, but adding in extra multimedia capabilities just isn't worth the lousy desktop experience, one that is so bad that quite frankly, it made Ubuntu seem like a good experience.

Now, I shouldn't leave this without noting there is some hope for the Playstation3 faithful. The Nouveau project has succeeded in some of the basic implementation of G80 support compiled under PowerPC. There is hope that a matured Nouveau driver might be capable of driving accelerated graphics on the PS3. So, if you want to be able to USE Linux on the PS3, please, go support Project Nouveau. http://nouveau.freedesktop.org/wiki/