Group-theoretic algorithms for matrix multiplication Export

@misc{citeulike:402464, abstract = {We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication exponent less than 3, the asymptotically fastest of which achieves exponent 2.41. We present two conjectures regarding specific improvements, one combinatorial and the other algebraic. Either one would imply that the exponent of matrix multiplication is 2.}, archivePrefix = {arXiv}, author = {Cohn, Henry and Kleinberg, Robert and Szegedy, Balazs and Umans, Christopher}, citeulike-article-id = {402464}, citeulike-linkout-0 = {http://arxiv.org/abs/math.GR/0511460}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.GR/0511460}, day = {18}, eprint = {math.GR/0511460}, keywords = {algorithm, cs, group\_theory, linear\_algebra, mathematics, matrix\_multiplication, strassen, tcs, theory}, month = {Nov}, posted-at = {2009-01-29 01:59:05}, priority = {2}, title = {Group-theoretic algorithms for matrix multiplication}, url = {http://arxiv.org/abs/math.GR/0511460}, year = {2005} }

TY - ELEC ID - citeulike:402464 L3 - citeulike-article-id:402464 N2 - We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication exponent less than 3, the asymptotically fastest of which achieves exponent 2.41. We present two conjectures regarding specific improvements, one combinatorial and the other algebraic. Either one would imply that the exponent of matrix multiplication is 2. TI - Group-theoretic algorithms for matrix multiplication KW - algorithm KW - cs KW - group_theory KW - linear_algebra KW - mathematics KW - matrix_multiplication KW - strassen KW - tcs KW - theory AU - Cohn, Henry AU - Kleinberg, Robert AU - Szegedy, Balazs AU - Umans, Christopher PY - 2005/Nov/18/ UR - http://arxiv.org/abs/math.GR/0511460 ER -