In the CUDA SDK, there is example code and presentation slides for an efficient one-dimensional reduction. I have also seen several papers on and implementations of one-dimensional reductions and prefix scans in CUDA.
Is there efficient CUDA code available for a reduction of a dense two-dimensional array? Pointers to code or pertinent papers would be appreciated.
matrix reduction may be somewhat simpler to implement, because row/column reduction to a vector can be done independently. You can let each thread handle column/row (depending on matrix major dimension orientation) and coalesce memory reads. I doubt you can buy much performance over that without going to texture/constant cache where locality may become important
I don't know what exactly the problem you try to solve, but actually you could simply think about 2D array as a long 1D array and use SDK code to reduce operation. Simple arrays in CUDA are just 1D memory blocks with special addressing rules - why wouldn't you take advantage of that opportunity.