Fast Rectangular Matrix Multiplication and Applications
نویسندگان
چکیده
First we study asymptotically fast algorithms for rectangular matrix multiplication. We begin with new algorithms for multiplication of an n_n matrix by an n_n matrix in arithmetic time O(n), |=3.333953..., which is less by 0.041 than the previous record 3.375477... . Then we present fast multiplication algorithms for matrix pairs of arbitrary dimensions, estimate the asymptotic running time as a function of the dimensions, and optimize the exponents of the complexity estimates. For a large class of input matrix pairs, we improve the known exponents. Finally we show three applications of our results:
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عنوان ژورنال:
- J. Complexity
دوره 14 شماره
صفحات -
تاریخ انتشار 1998