Have a personal or library account? Click to login
Convergence Analysis of a Three Step Newton-like Method for Nonlinear Equations in Banach Space under Weak Conditions Cover

Convergence Analysis of a Three Step Newton-like Method for Nonlinear Equations in Banach Space under Weak Conditions

Open Access
|Dec 2016

References

  1. [1] S. Amat, S. Busquier, and A. Grau-Sánchez, Maximum efficiency for a family of Newton-like methods with frozen derivatives and some application, Appl. Math. Comput. 219 (15), (2013), 7954 - 796310.1016/j.amc.2013.01.047
  2. [2] I.K. Argyros, Computational theory of iterative methods Ed. by C.K. Chui and L. Wuytack, Elsevier Publ. Co., New York, U.S.A, 2007
  3. [3] I.K.Argyros and S. George, Ball convergence of a sixth order iterative method with one parameter for solving equations under weak conditions, Calcolo, 53, (2016), 585-59510.1007/s10092-015-0163-y
  4. [4] I.K. Argyros and H. Ren, Improved local analysis for certain class of iterative methods with cubic convergence, Numerical Algorithms, 59, (2012), 505-52110.1007/s11075-011-9501-6
  5. [5] I.K.Argyros, Yeol Je Cho, and S. George, Local convergence for some third- order iterative methods under weak conditions, J. Korean Math. Soc. 53 (4), (2016), 781 - 79310.4134/JKMS.j150244
  6. [6] A. Cordero, J. Hueso, E. Martinez, and J. R. Torregrosa, A modified Newton- Jarratt's composition, Numer. Algor. 55, (2010), 87-9910.1007/s11075-009-9359-z
  7. [7] A. Cordero and J. R. Torregrosa, Variants of Newton's method for functions of several variables, Appl.Math. Comput. 183, (2006), 199-20810.1016/j.amc.2006.05.062
  8. [8] A. Cordero and J. R. Torregrosa, Variants of Newton's method using fifth order quadrature formulas, Appl.Math. Comput. 190, (2007), 686-69810.1016/j.amc.2007.01.062
  9. [9] G.M. Grau-Sanchez, A.Grau, and M.Noguera, On the computational efficiency index and some iterative methods for solving systems of non-linear equations, J. Comput. Appl Math. 236, (2011), 1259-126610.1016/j.cam.2011.08.008
  10. [10] H.H.Homeier, On Newton type methods with cubic convergence, J. Comput. Appl. Math. 176, (2005), 425-43210.1016/j.cam.2004.07.027
  11. [11] J.S. Kou, Y. T. Li, and X.H. Wang, A modification of Newton method with fifth-order convergence, J. Comput. Appl. Math. 209, (2007), 146-15210.1016/j.cam.2006.10.072
  12. [12] A.N. Romero, J.A. Ezquerro, and M .A. Hernandez, Approximacion de soluciones de algunas equacuaciones integrals de Hammerstein mediante metodos iterativos tipo, Newton, XXI Congresode ecuaciones diferenciales y aplicaciones, (2009)
  13. [13] W.C. Rheinboldt, An adaptive continuation process for solving systems of non- linear equations Ed. by A.N.Tikhonov et al. in Mathematical models and numerical methods, Banach Center, Warsaw Poland, 1977, 129-14210.4064/-3-1-129-142
  14. [14] J.R. Sharma and P.K. Gupta, An efficient fifth order method for solving systems of nonlinear equations, Comput. Math. Appl. 67, (2014), 591 - 60110.1016/j.camwa.2013.12.004
  15. [15] J.R. Sharma and R.K. Guha, Simple yet efficient Newton-like method for systems of nonlinear equations, Calcolo, 53, (2016), 451-47310.1007/s10092-015-0157-9
  16. [16] J.F.Traub, Iterative methods for the solution of equations, AMS Chelsea Publishing, 1982
DOI: https://doi.org/10.1515/awutm-2016-0013 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 37 - 46
Submitted on: Oct 16, 2016
Accepted on: Feb 12, 2016
Published on: Dec 30, 2016
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2016 Ioannis K. Argyros, Santhosh George, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.