5 ms·
Why do you say it will scale far beyond? Mat mul is N^3 as is eigenvalue solving. It's actually the second highest eigenvalue. The highest eigenvalue is always
by howeman 10y ago
Why do you say it will scale far beyond? Mat mul is N^3 as is eigenvalue solving.
It's actually the second highest eigenvalue. The highest eigenvalue is always 1 for stochastic matrices.
- j2kun 10y agoPower method is not matrix-matrix multiplication (which is not N^3, BTW [1]), but rather matrix-vector multiplication. So the power method is N^2*k where k is the number of iterations required to reach precision (usually polylogarithmic). All this being said, scalability is _obviously_ a non-issue when talking about a matrix of programming languages. All methods are constant time. [1]: https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Sub-cubic_algorithms https://en.wikipedia.org/wiki/Matrix_multiplication_algorith... Interesting tidbit: nobody can even prove it's not N^2 :)
- howeman 10y agoOh right, of course, because you're iterating the distribution. Duh. And yea, mat mul is not N^3 theoretically, but most implementations are. I've heard that some (mkl maybe) are 2.8, but haven't had someone point code to me. My personal attempts at implementing Strassen were slower than a tuned N^3 implementation, at least for matrices that fit into memory.