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Local convergence for some third-order iterative methods under weak conditions

조열제|Ioannis K. Argyros|Santhosh George
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회지 (Journal of the KMS)|제53권 제4호|pp. 781-793

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참고문헌

키워드

Newton methodlocal convergenceorder of convergence
주제분류수학

초록

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

Abstract

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

참고문헌 (30)

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