Computational complexity: on the geometry of polynomials and a theory of cost: II
SIAM Journal on Computing
On the worst-case arithmetic complexity of approximating zeros of polynomials
Journal of Complexity
On the efficiency of Newton's method in approximating all zeros of a system of complex polynomials
Mathematics of Operations Research
On a theorem of S. Smale about Newton's method for analytic mappings
Applied Mathematics Letters
An efficient algorithm for the complex roots problem
Journal of Complexity
Improvement of a convergence condition for the Durand-Kerner iteration
Journal of Computational and Applied Mathematics
New techniques for approximating complex polynomial zeros
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A Machine Method for Solving Polynomial Equations
Journal of the ACM (JACM)
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Path lengths in tree-child time consistent hybridization networks
Information Sciences: an International Journal
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Several different uses of Newton's method in connection with the Fundamental Theorem of Algebra are pointed out. Theoretical subdivision schemes have been combined with the numerical Newton iteration to yield fast root-approximation methods together with a constructive proof of the fundamental theorem of algebra. The existence of the inverse near a simple zero may be used globally to convert topological methods like path-following via Newton's method to numerical schemes with probabilistic convergence. Finally, fast factoring methods which yield root-approximations are constructed using some algebraic Newton iteration for initial factor approximations.