3 ms·
Is it yet known what the optimal sequence is for 3x3 matrix multiplication (for noncommuting entries, of course)?
by wbhart 8y ago
Is it yet known what the optimal sequence is for 3x3 matrix multiplication (for noncommuting entries, of course)?
- wLMeOv2qjsFOjZG 8y agoNo!
- stochastic_monk 8y agoWouldn’t this be easy to explore exhaustively? 27! is ~1e26, but most of these orderings are obviously terrible ideas.
- wLMeOv2qjsFOjZG 8y agoFor 2x2 matrix multiplication, it is known that Strassen's algorithm is optimal in the sense that there exists no algebraic circuit that uses only 6 "scalar" multiplications. I took your question to ask whether for 3x3 matrix multiplication, the minimum number of scalar multiplications required was similarly known. It is not, and there are more options to take into account than just orderings.