Horner Systems: How to efficiently evaluate non-commutative polynomials (by matrices)
arXiv:1910.01401
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.
arXiv comment25 pages, 1 table
References in corpus (6)
- Fast matrix multiplication is stable
- Factorization theory: From commutative to noncommutative settings
- On the Factorization of Non-Commutative Polynomials (in Free Associative Algebras)
- Linearizing the Word Problem in (some) Free Fields
- Free Fractions: An Invitation to (applied) Free Fields
- A Factorization Theory for some Free Fields