Geometry of polynomials and root-finding via path-lifting
نویسندگان
چکیده
منابع مشابه
Mcmullen’s Root-finding Algorithm for Cubic Polynomials
We show that a generally convergent root-finding algorithm for cubic polynomials defined by C. McMullen is of order 3, and we give generally convergent algorithms of order 5 and higher for cubic polynomials. We study the Julia sets for these algorithms and give a universal rational map and Julia set to explain the dynamics.
متن کاملEfficient Root Finding of Polynomials over Fields of Characteristic 2
Root finding is the most time-consuming stage of McEliece cryptosystem decryption. The best method to find the zeroes of a polynomial for cryptographic parameters is the Berlekamp Trace Algorithm (BTA). Our idea is to mix BTA with ad-hoc methods proposed by Zinoviev. We obtain a significant gain in terms of time complexity for finding roots and so we decrease McEliece decryption time. This pape...
متن کاملFinding Roots of Polynomials Based on Root Moments
This paper proposes using root moment method to find the roots of arbitrary polynomials. It has been proved that feedforward neural networks (FNN) trained with constrained learning (CL) back propagation (BP) algorithm can be used to estimate the distributions of roots of polynomials. It has been found, however, that using the different priori information implicit in the polynomials for CL-BP al...
متن کاملChaotic Root-Finding for a Small Class of Polynomials
In this paper we present a new closed-form solution to a chaotic difference equation, yn+1 = a2y 2 n + a1yn + a0 with coefficient a0 = (a1 − 4)(a1 + 2)/(4a2), and using this solution, show how corresponding exact roots to a special set of related polynomials of order 2, p ∈ N with two independent parameters can be generated, for any p.
متن کاملChaotic Root-Finding for a Small Class of Polynomials
In this paper we present a new closed-form solution to a chaotic difference equation, yn+1 = a2y 2 n + a1yn + a0 with coefficient a0 = (a1 − 4)(a1 + 2)/(4a2), and using this solution, show how corresponding exact roots to a special set of related polynomials of order 2, p ∈ N with two independent parameters can be generated, for any p.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinearity
سال: 2018
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/aa8ca8