On the construction of some tri-parametric iterative methods with memory

详细信息    查看全文

• 作者：Taher Lotfi ; Fazlollah Soleymani ; Mohammad Ghorbanzadeh…
• 关键词：Tri ; parametric ; Self ; accelerator ; R ; order ; With memory ; 65H05
• 刊名：Numerical Algorithms
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：70
• 期：4
• 页码：835-845
• 全文大小：226 KB
• 参考文献：1.Cordero, A., Lotfi, T., Mahdiani, K., Torregrosa, J.R.: A stable family with high order of convergence for solving nonlinear equations. Appl. Math. Comput. 254, 240鈥?51 (2015)MathSciNet CrossRef
  2.D啪uni膰, J., Petkovi膰, M.S., Petkovi膰, L.D.: Three-point methods with without memory for solving nonlinear equations. Appl. Math. Comput. 218, 4917鈥?927 (2012)MathSciNet CrossRef MATH
  3.D啪uni膰, J.: On efficient two-parameter methods for solving nonlinear equations. Numer. Algor. 63, 549鈥?69 (2013)CrossRef MATH
  4.Geum, Y.H., Kim, Y.I.: A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function. J. Comput. Appl. Math. 235, 3178鈥?188 (2011)MathSciNet CrossRef MATH
  5.Geum, Y.H., Kim, Y.I.: A family of optimal sixteenth-order multipoint methods with a linear fraction plus a trivariate polynomial as the fourth-step weighting function. Comput. Math. Appl. 61, 3278鈥?287 (2011)MathSciNet CrossRef MATH
  6.Grau-S谩nchez, M., Noguera, M., Grau, 圈., Herrero, J.R.: On new computational local orders of convergence. Appl. Math. Lett. 25, 2023鈥?030 (2012)MathSciNet CrossRef MATH
  7.Iliev, A., Kyurkchiev, N.: Nontrivial methods in numerical analysis: selected topics in numerical analysis. LAP LAMBERT Acad. Pub., Saarbrcken (2010)
  8.Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Math. 21, 634鈥?51 (1974)MathSciNet CrossRef
  9.Lotfi, T., Shateyi, S., Hadadi, S.: Potra-Pt谩k iterative method with memory. ISRN Math. Anal. Vol. 2014, Article ID 697642, 6 pages
  10.Lotfi, T., Magre帽谩n, 脕.A., Mahdiani, K., Javier Rainer, J.: A variant of Steffensen-King鈥檚 type family with accelerated sixth-order convergence and high efficiency index: Dynamic study and approach. Math. Comput. Appl. 252, 347鈥?53 (2015)CrossRef
  11.Petkovi膰, M.S., Neta, B., Petkovi膰, L.D., D啪uni膰, J.: Multipoint methods for solving nonlinear equations: A survey. Appl. Math. Comput. 226, 635鈥?60 (2014)MathSciNet CrossRef
  12.Sharma, J.R., Guha, R.K., Gupta, P.: Some efficient derivative free methods with memory for solving nonlinear equations. Appl. Math. Comput. 219, 699鈥?07 (2012)MathSciNet CrossRef MATH
  13.Soleymani, F., Babajee, D.K.R., Shateyi, S., Mosta, S.S.: Construction of optimal derivative-free techniques without memory. J. Appl. Math. Volume 2012, Article ID 497023, 24 pages
  14.Soleymani, F., Sharifi, M., Shateyi, S., Haghani, F.K.: A class of Steffensen-type iterative methods for nonlinear systems, J. Appl. Math., Volume 2014, Article ID 705375, 9 pages.
  15.Soleymani, F., Lotfi, T., Tavakoli, E., Khaksar Haghani, F.: Several iterative methods with memory using self-accelerators. Appl. Math. Comput. 254, 452鈥?58 (2015)MathSciNet CrossRef
  16.Steffensen, J.F.: Remarks on iteration. Skand. Aktuarietidskr 16, 64鈥?2 (1933)
  17.Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice Hall, New York (1964)MATH
  18.Wang, X., Zhang, T.: High-order Newton-type iterative methods with memory for solving nonlinear equations. Math. Commun. 19, 91鈥?09 (2014)MathSciNet MATH
  19.Zheng, Q., Li, J., Huang, F.: Optimal Steffensen-type families for solving nonlinear equations. Appl. Math. Comput. 217, 9592鈥?597 (2011)MathSciNet CrossRef MATH
  
• 作者单位：Taher Lotfi (1)
  Fazlollah Soleymani (1)
  Mohammad Ghorbanzadeh (2)
  Paria Assari (1)
  
  1. Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
  2. Department of Mathematics, Imam Reza International University, Mashhad, Iran
  
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing
  Algorithms
  Mathematics
  Algebra
  Theory of Computation
  
• 出版者：Springer U.S.
• ISSN：1572-9265

文摘

In this work, two-step methods with memory by applying three self-accelerator parameters are proposed and analyzed. In fact, we hit the high bound \(7.77200^{\frac {1}{3}}\approx 1.98082\) as the efficiency index. Theoretical results are then supported by numerical examples. Keywords Tri-parametric Self-accelerator R-order With memory