TITLE: Has there been a rigorous analysis of Strassen's algorithm?
QUESTION [10 upvotes]: According to Wikipedia, Strassen's Algorithm runs in $O(N^{2.807})$ time.  Has anyone seen a more rigorous analysis displaying constants, possibly in a specific language such as C or Java?  
I realize this will vary from language to language, machine to machine etc, but does anyone know of an approximate input size where Strassen's algorithm starts to outperform regular matrix multiplication?  
I think this may belong on the computer science stack exchange but since it is somewhat mathematical I thought I would post it here.

REPLY [3 votes]: From a google search [crossover strassen matrix multiplication], I've found that experiments have found the crossover point to be from n = 8 to n = 20.
However, at some point in analysis of algorithms you jump from manipulating mathematical concepts straight to just running things experimentally and recording values and times. At that point it is not really called analysis of algorithms, but instead plain old engineering where you manipulate things other than the basic algorithm (agressively optimizing compiling, caching strategies, the speed of memory components, hardware parallelization, the cooling system, etc). Then the variables to consider are too many and underspecified to make an analytic (on paper) calculation, and you just have to compare using runtime data.