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Newtonian Vector Field

The vector field

N_f(z)=-(f(z))/(f^'(z))

arising in the definition of the Newtonian graph of a complex univariate polynomial f (Smale 1985, Shub et al. 1988, Kozen and Stefánsson 1997).

See also

Newton's Method, Newtonian Graph, Vector Field

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References

Kozen, D. and Stefánsson, K. "Computing the Newtonian Graph." J. Symb. Comput. 24, 125-136, 1997.Shub, M.; Tischler, D.; Williams, R. F. "The Newtonian Graph of a Complex Polynomial." SIAM J. Math. Anal. 19, 246-256, 1988.Smale, S. "On the Efficiency of Algorithms of Analysis." Bull. Amer. Math. Soc. 13, 87-121, 1985.

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Newtonian Vector Field

Cite this as:

Weisstein, Eric W. "Newtonian Vector Field." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NewtonianVectorField.html

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