Duality Applied to the Complexity of Matrix Multiplication and Other Bilinear Forms.
Abstract
The paper considers the complexity of bilinear forms in a noncommutative ring. The dual of a computation is defined and applied to matrix multiplication and other bilinear forms. It is shown that the dual of an optimal computation gives an optimal computation for a dual problem. An nxm by mxp matrix product is shown to be the dual of an nxp by pxm or an mxn by nxp matrix product implying that each of the matrix products requires the same number of multiplications to compute. Finally an algorithm for computing a single bilinear form over a noncommutative ring with a minimum number of multiplications is derived by considering a dual problem. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1972
- Accession Number
- AD0751088
Entities
People
- Jean Musinski
- John Hopcroft
Organizations
- Department of Computer Science, Cornell University