### Abstract

At the heart of a number of arithmetic complexity problems are some basic questions in tensor analysis. Questions regarding the complexity of multiplication operations which are n-linear are most easily studied in a tensor analytic framework. Certain results of tensor analysis are used in this paper to provide insight into the solution of some of these problems. Methods are given to determine a partial ordering on the set of tensors corresponding to a partial ordering with respect to complexity on the set of n-linear operations. Different classes of algorithms for evaluating n-linear operations are studied and a generalized cost criterion is used. Algorithms are given for determining the rank of a class of third order tensors and a canonical form for such tensors is presented. Bounds on the complexity of a wide class of operations are also derived.

Original language | English (US) |
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Pages | 92-102 |

Number of pages | 11 |

DOIs | |

State | Published - Jan 1 1973 |

Event | 14th Annual Symposium on Switching and Automata Theory - Iowa City, United States Duration: Oct 15 1973 → Oct 17 1973 |

### Conference

Conference | 14th Annual Symposium on Switching and Automata Theory |
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Country | United States |

City | Iowa City |

Period | 10/15/73 → 10/17/73 |

### All Science Journal Classification (ASJC) codes

- Computational Theory and Mathematics
- Control and Optimization
- Theoretical Computer Science
- Artificial Intelligence

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## Cite this

*On the optimal evaluation of a set of n-linear forms*. 92-102. Paper presented at 14th Annual Symposium on Switching and Automata Theory, Iowa City, United States. https://doi.org/10.1109/SWAT.1973.4569733