GPU programming, part II

It looks like the programming of GPUs is taking off. This article shows an improvement of 3.5 times for a 1500 by 1500 matrix multiplication. This is not enough for many different reasons. One of the reason is Moores law which basically states that in about a year this performance will be nulled by the speed of the CPU. Well, one would say, if they were to use a 10000 by 10000 element matrix the speedup would have been more impressive and I would have to agree. However, they are not that many engineering problems that require 10000 by 10000 element matrix multiplication. Generally one wants to rely of sparse solvers because a full system with a high number of elements is likely having issues with precision. The only class of problems that deals with that many elements is integral equation, however, there again, the projection of the problem on a reasonable basis like wavelet or curvelet should sparsify the system at hand.