2013/07/31 by João Ferreira Alves, João F. Alves, António Bravo +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebra over a field #Algebraic number #Applied mathematics #Context (archaeology) #Geometry #Linear algebra #Linear system #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Order (exchange) #Polynomial and algebraic computation #Pure mathematics #Recurrence relation #math.DS #math.RA #msc:15A15 #msc:39A06
paper · pdf · doi:10.1016/j.laa.2015.02.035
18 Pages
arxiv created 2015/03/05 · arxiv updated 2015/03/06 · openalex publication_date 2015/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Infinite order linear recurrences are studied via kneading matrices and kneading determinants. The concepts of kneading matrix and kneading determinant of an infinite order linear recurrence, introduced in this work, are defined in a purely linear algebraic context. These concepts extend the classical notions of Frobenius companion matrix to infinite order linear recurrences and to the associated discriminant of finite order linear recurrences. Asymptotic Binet formulas are deduced for general classes of infinite order linear recurrences as a consequence of the analytical properties of the generating functions obtained for the solutions of these infinite order linear recurrences.