Have a personal or library account? Click to login
Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions Cover

Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions

Open Access
|Dec 2020

References

  1. [1] I. K. Argyros, Computational theory of iterative methods, Series: Studies in Computational Mathematics, 15, Editors: C.K.Chui and L. Wuytack, Elsevier Publ. Co., New York, U.S.A, 2007
  2. [2] 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
  3. [3] I. K. Argyros, Y. J. 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
  4. [4] I. K. Argyros and S. George, Ball convergence of a sixth order iterative method with one parameter for solving equations under weak conditions, Calcolo, DOI 10.1007/s10092-015-0163-y
  5. [5] A. Cordero, J. Hueso, E. Martinez, and J. R. Torregrosa, A modified Newton-Jarratt’s composition, Numerical Algorithms, 55, (2010), 87-9910.1007/s11075-009-9359-z
  6. [6] 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
  7. [7] 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
  8. [8] 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
  9. [9] H. H. H. Homeier, A modified Newton method with cubic convergence, the multivariable case, J. Comput. Appl. Math., 169, (2004), 161-16910.1016/j.cam.2003.12.041
  10. [10] H. 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 equaciones integrals de Hammerstein mediante metodos iterativos tipo. Newton, XXI Congreso de ecuaciones diferenciales y aplicaciones, Universidad de Castilla-La Mancha, 2009
  13. [13] W. C. Rheinboldt, An adaptive continuation process for solving systems of nonlinear equations, Mathematical Models and Numerical Methods, Ed. by A. N. Tikhonov et al., Banach Center, Warsaw, Poland, 1977, 129-14210.4064/-3-1-129-142
  14. [14] J. R. Sharma and P. K. Gupta, An e cient 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. F. Traub, Iterative methods for the solution of equations, AMS Chelsea Publishing, 1982
  16. [16] X. Y. Xiao and H. W. Yin, Increasing the order of convergence for iterative methods to solve non-linear systems, Calcolo, DOI10.1007/s10092-015-0149-9
DOI: https://doi.org/10.2478/awutm-2019-0006 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 53 - 65
Published on: Dec 8, 2020
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2020 Ioannis K. Argyros, Santhosh George, Shobha M. Erappa, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.