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- W154622810 abstract "A polynomial $fin complex[z]$ defines a vector field $N_f(z) = -f(z)/f''(z)$ on $complex$. Certain degenerate curves of flow in $N_f$ give the edges of the Newtonian graph, as defined by cite{Sma85}. These give a relation between the roots of $f$ and $f''$, much similar to the linear order, when $f$ has real roots only. We give a purely algebraic algorithm to compute the Newtonian graph and the basins of attraction in the Newtonian field. The resulting structure can be used to query whether two points in $complex$ are within the same basin of attraction. This gives us an algebraic approach to root-finding using Newton''s method. This method extends to rational functions and more generally to any functions on $complex$ whose flow is algebraic over $complex(e)$." @default.
- W154622810 created "2016-06-24" @default.
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- W154622810 date "1993-10-01" @default.
- W154622810 modified "2023-09-27" @default.
- W154622810 title "Computing the Newtonian Graph (Extended abstract)" @default.
- W154622810 hasPublicationYear "1993" @default.
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