Horner Systems: How to efficiently evaluate non-commutative polynomials (by matrices)
Rings and Algebras
2019-10-04 v1 Optimization and Control
Abstract
By viewing non-commutative polynomials, that is, elements in free associative algebras, in terms of linear representations, we generalize Horner's rule to the non-commutative (multivariate) setting. We introduce the concept of Horner systems (which has parallels to that of companion matrices), discuss their construction and show how they enable the efficient evaluation of non-commutative polynomials by matrices.
Cite
@article{arxiv.1910.01401,
title = {Horner Systems: How to efficiently evaluate non-commutative polynomials (by matrices)},
author = {Konrad Schrempf},
journal= {arXiv preprint arXiv:1910.01401},
year = {2019}
}
Comments
25 pages, 1 table