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Neta, Beny; Scott, Melvin; Chun, Changbum

Basins of attraction for several methods to find simple roots of nonlinear equations. (English) Zbl 1250.65067

Appl. Math. Comput. 218, No. 21, 10548-10556 (2012).
Summary: There are many methods for solving a nonlinear algebraic equation. The methods are classified by the order, informational efficiency and efficiency index. Here, we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss several third and fourth order methods to find simple zeros. The relationship between the basins of attraction and the corresponding conjugacy maps is discussed in numerical experiments. The effect of the extraneous roots on the basins is also discussed.

Cited in 73 Documents

MSC:

65H05 Numerical computation of solutions to single equations

Keywords:

basin of attraction; simple roots; nonlinear equations; Halley method; super Halley method; modified super Halley method; King’s family of methods; numerical experiments
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\textit{B. Neta} et al., Appl. Math. Comput. 218, No. 21, 10548--10556 (2012; Zbl 1250.65067)
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References:

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