2019/10/03 by Konrad Schrempf, Schrempf, Konrad
Computer Science · Engineering · Mathematics · #47A56 (Secondary) #68W30 (Primary) 16Z05 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #FOS: Mathematics #Mathematics and Applications #Optimization and Control (math.OC) #Polynomial and algebraic computation #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.OC #math.RA #msc:16Z05 #msc:47A56 #msc:68W30
paper · pdf · doi:10.48550/arxiv.1910.01401
25 pages, 1 table
arxiv created 2019/10/03 · openalex publication_date 2019/10/03 · arxiv updated 2019/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.