Polynomial root-finding algorithms and branched covers
Myong-Hi Kim, Scott Sutherland
Abstract
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree d with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that computes an ε-factorization of the polynomial which has an arithmetic complexity of d2( d)2 + d( d)2|ε|. At the present time (1993), this complexity is the best known in terms of the degree.
Create a lesson
Related papers
GPU-Accelerated Orbit Propagation with High-Fidelity Solar Radiation Pressure Modeling
Leandro Zardaín, Ariadna Farrés, Anna Puig et al.
A three-dimensional corner configuration involving the Omega function
Zhuowen Guo, Rongzhong Xiao, Shuhao Zhang
Hereditary Lowerability of Topological Dynamical Systems
Xiaochen Wang
A generalized push-forward construction of Sinai-Ruelle-Bowen measures
Grigorii Dvorkin
Orbital counting for relatively Anosov groups
Richard Canary, Tengren Zhang, Feng Zhu et al.
Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators
Maximiliano Hertel, Ilja Klebanov, Manuel Schaller et al.