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Basin attractors for various methods for multiple roots. (English) Zbl 1244.65068
Summary: There are several methods for approximating the multiple zeros of a nonlinear function when the multiplicity is known. 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 all known methods of orders two to four and present the basin of attraction for several examples.

65H05Single nonlinear equations (numerical methods)
65Y20Complexity and performance of numerical algorithms
Full Text: DOI
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