algorithm - Complexity of large matrix multiplication -


what time complexity of fastest algorithm known today multiply large matrices?

what theoretical optimal time complexity reached?

this active area of research, answer may out of date. :-)

to best of knowledge, current fastest matrix multiplication algorithm runs in time o(n2.373), due result virginia williams. algorithm large family of algorithms give rise complex nonlinear system of equations give overall time bound, , in fact there people doing work right trying see how improve bound finding better , better solutions equations. believe algorithm of theoretical interest, though.

the holy grail of matrix multiplication o(n2)-time matrix multiplication algorithm, , whether such algorithm exists still open problem. theoretical limit, since o(n2)-time algorithm couldn't read entries of matrices multiply.

hope helps!


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