论文信息 - On the Additive Complexity of 2 x 2 Matrix Multiplication

On the Additive Complexity of 2 x 2 Matrix Multiplication

Abstract Probert proved that 15 additive operations are necessary and sufficient to multiply two 2 × 2 matrices over the binary field by a bilinear algorithm using 7 non-scalar multiplications. We prove this result for an arbitrary field.

Nader H. Bshouty | N. Bshouty

[1] V. Strassen. Gaussian elimination is not optimal , 1969 .

[2] John E. Hopcroft,et al. Duality Applied to the Complexity of Matrix Multiplication and Other Bilinear Forms , 1973, SIAM J. Comput..

[3] Robert L. Probert. On the Additive Complexity of Matrix Multiplication , 1976, SIAM J. Comput..

[4] Shmuel Winograd,et al. On multiplication of 2 × 2 matrices , 1971 .

[5] Hans F. de Groote. On Varieties of Optimal Algorithms for the Computation of Bilinear Mappings I. The Isotropy Group of a Bilinear Mapping , 1978, Theor. Comput. Sci..

[6] Hans F. de Groote. On Varieties of Optimal Algorithms for the Computation of Bilinear Mappings. II. Optimal Algorithms for 2x2-Matrix Multiplication , 1978, Theor. Comput. Sci..

[7] David G. Kirkpatrick,et al. Addition Requirements for Matrix and Transposed Matrix Products , 1988, J. Algorithms.

[8] Ephraim Feig,et al. On the direct sum conjecture , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).