Constructing two-step iterative methods with and without memory

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• 作者：Taher Lotfi (1)
  Katayoun Mahdiani (1)
  Parisa Bakhtiari (2)
  Fazlollah Soleymani (3)
  
  1. Department of Applied Mathematics ; Hamedan Branch ; Islamic Azad University ; Hamedan ; Iran
  2. Young Researchers and Elite Club ; Hamedan Branch ; Islamic Azad University ; Hamedan ; Iran
  3. Department of Mathematics ; Zahedan Branch ; Islamic Azad University ; Zahedan ; Iran
  
• 关键词：iterative methods ; R ; order ; without memory ; with memory ; computational efficiency
• 刊名：Computational Mathematics and Mathematical Physics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：55
• 期：2
• 页码：183-193
• 全文大小：199 KB
• 参考文献：1. Kyurkchiev, N, Iliev, A (2013) On some multipoint methods arising from optimal in the sense of Kung-Traub algorithms. Int. J. Math. Meth. Models Biosci. 2: pp. 1-7
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  7. F. Soleymani and P. S. Stanimirovi, 鈥淎 higher order iterative method for computing the Drazin inverse,鈥?Sci. World J. 2013, Article ID 708647, 11 pages (2013).
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1555-6662

文摘

Some new iterative methods without memory are constructed to reach the optimal convergence order four using only three function evaluations to solve nonlinear equations. Per full cycle, each method from the derived classes is derivative-free. We further extend the derived classes of methods to contribute some schemes with memory, without any additional evaluation of the function. Hence, with a same cost, the contributed methods with memory possess higher R-orders and better efficiency indices. In order to attest the efficiency of the obtained methods, we employ numerical comparisons.