Another approach to this is hands-on comparison. You can get a library like Blitz++ (http://www.oonumerics.org/blitz/) which - I've been told - implements aggressive optimisations for numeric/scientific computing, then write some simple programs doing operations of interest to you (e.g. matrix multiplications). As you use Blitz++ to perform them, write your own class that does the same, and if Blitz++ proves faster start investigating it's implementation until you realise why. (If yours is significantly faster you can tell the Blitz++ developers!)
You should end up learning about a lot of things, for example:
- memory cache access patterns
- expression templates (there are some bad links atop Google search results re expression templates - the key scenario/property you want to find discussion of is that they can encode many successive steps in a chain of operations such that they all be applied during one loop over a data set)
- some CPU-specific instructions (though I haven't checked they've used such non-portable techniques)...
