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(n 2.7743).
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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