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A general three-step class of optimal iterations for nonlinear equations. (English) Zbl 1235.74002
Summary: Many of the engineering problems are reduced to solve a nonlinear equation numerically, and as a result, an especial attention to suggest efficient and accurate root solvers is given in literature. Inspired and motivated by the research going on in this area, this paper establishes an efficient general class of root solvers, where per computing step, three evaluations of the function and one evaluation of the first-order derivative are used to achieve the optimal order of convergence eight. The without-memory methods from the developed class possess the optimal efficiency index 1.682. In order to show the applicability and validity of the class, some numerical examples are discussed.
MSC:
74-04Machine computation, programs (mechanics of deformable solids)
74S30Other numerical methods in solid mechanics
65H04Roots of polynomial equations (numerical methods)