This dissertation reviews the theory of fast matrix multiplication from a multilinear-algebraic point of view, as
well as recent fast matrix multiplication algorithms based on discrete Fourier transforms over nite groups.
To this end, the algebraic approach is described in terms of group algebras over groups satisfying the triple
product Property, and the construction of such groups via uniquely solvable puzzles.
The higher order singular value decomposition is an important decomposition of tensors that retains some of
the properties of the singular value decomposition of matrices. However, we have proven a novel negative result
which demonstrates that the higher order singular value decomposition yields a matrix multiplication algorithm
that is no better than the standard algorithm. / Mathematical Sciences / M. Sc. (Applied Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/20180 |
| Date | January 2015 |
| Creators | Gouaya, Guy Mathias |
| Contributors | Hardy, Y. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | 1 online resource (vi, 52 leaves) |
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