Chapter 2

Two-point methods

This chapter is devoted to two-point root-finding methods. Traub’s study (Traub, 1964) of two-point methods of third order is the first systematic investigation of multipoint methods. Although these methods are not optimal, in Section 2.1 we give a short review of Traub’s methods for their great influence to the later development of multipoint methods. To demonstrate developing techniques, several different derivations of the Ostrowski method originally proposed in 1960 (the first two-point method of order four) are presented in Section 2.2. Derivation and convergence analysis of two families of optimal two-point methods, proposed by the authors of this book, are presented in Sections 2.3 and 2.4. These families give ...

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