The bilinear complexity and practical algorithms for matrix multiplication
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A method for deriving bilinear algorithms for matrix multiplication is proposed. New estimates for the bilinear complexity of a number of problems of the exact and approximate multiplication of rectangular matrices are obtained. In particular, the estimate for the boundary rank of multiplying 3 × 3 matrices is improved and a practical algorithm for the exact multiplication of square n × n matrices is proposed. The asymptotic arithmetic complexity of this algorithm is O(n2.7743).
Keywordsbilinear complexity rank of the matrix multiplication problem boundary rank algorithms for exact and approximate matrix multiplication least-squares method objective function
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