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MULTIPOINT METHODS FOR SOLVING NONLINEAR EQUATIONS by Jovana Dzunic, Ljiljana Petkovic, Beny Neta, Miodrag Petkovic

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Chapter 4

Three-point optimal methods

As noted in the previous chapter, optimal multipoint methods of order higher than four were stated by Kung and Traub (1974). In the next 33 years many three-point methods requiring image were constructed, but their order did not reach optimal order image, see Chapter 3. However, it is worth noting that an optimal family of three-point methods was implicitly given in Neta’s paper (Neta, 1981) as a composite part of a four-point family of order sixteen, but neither the author emphasized and announced this fact nor other authors ...

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