2019/03/25 by Mario DeFranco, DeFranco, Mario · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1903.10697
openalex publication_date 2019/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present generalizations of the Newton-Raphson-Simpson method. Specifically, for a positive integer m and the sequence of coefficients of a Taylor series of a function f(z), we define an algorithm we denote by NRS(m) which is a way to evaluate, in our terminology, a sum of m formal zeros of f(z). We prove that NRS(1) yields the familiar iterations of the Newton-Raphson-Simpson method. We also prove that NRS(m) is way to evaluate certain \mathscrA-hypergeometric series defined by Sturmfels. In order to define these algorithms, we make use of combinatorial objects which we call trees with negative vertex degree.