Why is a naïve C++ matrix multiplication 100 times slower than BLAS?

Question

I am taking a look at large matrix multiplication and ran the following experiment to form a baseline test:

1. Randomly generate two 4096x4096 matrixes X, Y from

Answer 1

Strassen's algorithm has two advantages over the naïve algorithm:

1. Better time complexity in terms of number of operations, as other answers correctly point out;
2. It is a cache-oblivious algorithm. The difference in number of cache misses is in the order of B*M½, where B is the cache line size and M is the cache size.

I think that the second point accounts for a lot for the slowdown you are experiencing. If you are running your application under Linux, I suggest you run them with the perf tool, which tells you how many cache misses the program is experiencing.