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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Efficient numerical methods of Aitken type and their dynamics
P. Jain, P. B. Chand, K. Sethi Department of Mathematics,
South Asian University,
Akbar Bhawan, Chanakya Puri, New Delhi-110021, India
Аннотация:
In this paper, we derive some general Aitken type methods. These methods involve arbitrary methods of orders $p$ and $q$ which enable us to construct the method of any desired order. Further, it is shown that these methods can be combined with generalized secant method and as result, in the limiting case, the efficiency can be increased to $2$. We also discuss the stability of the iterative method with the help of basins of attraction in the complex plane. Some numerical examples are provided in support of the theoretical results.
Ключевые слова и фразы:
Steffensen method, Aitken method, secant method, dynamics, fixed and critical points, basin of attraction.
Поступила в редакцию: 26.09.2017
Образец цитирования:
P. Jain, P. B. Chand, K. Sethi, “Efficient numerical methods of Aitken type and their dynamics”, Eurasian Math. J., 9:3 (2018), 58–72
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj305 https://www.mathnet.ru/rus/emj/v9/i3/p58
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