Most of Matlab calculations are homework or simulations. Generally speaking the real world will add more errors then double floating points will reduce.
Honestly GNU Octave has been a surprisingly fast developing product. Matlab only got GPU acceleration 2 years ago (according to my buddy who uses Matlab) (which is very fast for a GNU project). A lot of academics are picking up on it, even professors recommending it.
I think the most glowing recommendation I heard was, "Well its free, and free goes along way when you're living on a research stipend."
Double-precision is a good default for a tool like Octave, but I agree that single-precision can be plenty accurate for a lot of uses. It's often just not worth the added time and code complexity to determine where single-precision should be used.
Single precision is about 2.5x faster than double precision on current GPUs (for matrix multiplication, which is compute dominated). It really depends on the application, but in my experience more often than not the only reason you are using GPUs is because you want to squeeze out every last ounce of performance. In these cases, single precision makes a lot of sense (assuming you're algorithm doesn't depend heavily on 64 bits of precision).
Within the neural nets community, single precision is almost always used (at least on GPUs).
it could very easily run double precision, but then they'd have to use their tesla cards to run it, and at several thousand dollars a piece, wont be quite as attractive to the user..
Consumer GPUs can do double-precision. At the high end, consumer parts usually (though not always) get crippled performance relative to their pro counterparts, but for the low and mid-range chips even the workstation cards have lackluster double-precision performance.
Is single-precision computations useful in the context where GNU Octave is generally used?