Iterative methods for nonlinear equations and their semilocal convergence

Abstract

We are concerned with the numerical methods for nonlinear equation and their semilocal convergence in this paper. The construction techniques of iterative methods are induced by using linear approximation, integral interpolation, Adomian series decomposition, Taylor expansion, multi-step iteration, etc. The convergent conditions and proof methods, including majorizing sequences and recurrence relations, in semilocal convergence of iterative methods for nonlinear equations are discussed in the theoretical analysis. The majorizing functions, which are used in majorizing sequences, are also discussed in this paper.

Keywords

Nonlinear equation / numerical method / semilocal convergence / Newton method / Banach space

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