References

  1. Argyros I.K. Convergence and applications of Newton-type iterations. Springer-Verlag, New York, 2008.
  2. Argyros I.K., Magreñán Á.A. A contemporary study of iterative methods. Convergence, dynamics and applications. Academic Press, London, 2019. doi:10.1016/C2015-0-04301-5
  3. Argyros I.K., Shakhno S. Extended Two-Step-Kurchatov method for solving Banach space valued nondifferentiable equations. Int. J. Appl. Math. Comput. Math. 2020, 6 (2), 32. doi:10.1007/s40819-020-0784-y
  4. Argyros I.K., Shakhno S.M., Yarmola H.P. Extended semilocal convergence for the Newton-Kurchatov method. Mat. Stud. 2020, 53 (1), 85–91. doi:10.30970/ms.53.1.85-91
  5. Argyros I.K., Shakhno S., Yarmola H. Improving convergence analysis of the Newton–Kurchatov method under weak conditions. Comput. 2020, 8 (1), 8. doi:10.3390/computation8010008
  6. Cãtinac E. On some iterative methods for solving nonlinear equations. Rev. Anal. Numér. Théor. Approx. 1994, 23 (1), 47–53.
  7. Dennis J.E.Jr., Schnabel R.B. Numerical methods for unconstrained optimization and nonlinear equations. SIAM, Philadelphia, 1996.
  8. Hernández M.A. Rubio M.J. A uniparametric family of iterative processes for solving nondiffrentiable operators. J. Math. Anal. Appl. 2002, 275 (2), 821–834. doi:10.1016/S0022-247X(02)00432-8
  9. Hernández-Verón M.A., Rubio M.J. On the local convergence of Newton-Kurchatov-type method for non-differentiable operators. Appl. Math. Comput. 2017, 304 (1), 1–9. doi:10.1016/j.amc.2017.01.010
  10. Ortega J.M., Rheinboldt W.C. Iterative solution of nonlinear equations in several variables. Acad. Press, San Diego, 1970.
  11. Ren H., Argyros I.K. Local convergence of a secant type method for solving least squares problems. Appl. Math. Comput. 2010, 217 (8), 3816–3824. doi:10.1016/j.amc.2010.09.040
  12. Ren H., Argyros I.K., Hilout S. A derivative free iterative method for solving least squares problems. Numer. Algor. 2011, 58 (4), 555–571. doi:10.1007/s11075-011-9470-9
  13. Shakhno S.M. Gauss-Newton-Kurchatov method for solving nonlinear least squares problems. J. Math. Sci. 2020, 247 (1), 58–72. doi:10.1007/s10958-020-04789-y (translation of Mat. Metody Fiz.-Mekh. Polya 2017, 60 (4),–62. (in Ukrainian))
  14. Shakhno S.M., Gnatyshyn O.P. Iterative-difference methods for solving nonlinear least-squares problem. In:Arkeryd L., Bergh J., Brenner P., Pettersson R. (Eds.) Progress in Industrial Mathematics at ECMI 98, Teubner, Stuttgart, 1999, 287–294.
  15. Shakhno S.M., Iakymchuk R.P., Yarmola H.P. An iterative method for solving nonlinear least squares problems with nondifferentiable operator. Mat. Stud. 2017, 48 (1), 97–107. doi:10.15330/ms.48.1.97-107
  16. Shakhno S.M., Yarmola H.P., Shunkin Yu.V. Convergence analysis of the Gauss-Newton-Potra method for nonlinear least squares problems. Mat. Stud. 2018, 50 (2), 211–221. doi:10.15330/ms.50.2.211-221
  17. Shakhno S.M., Shunkin Yu.V. One combined method for solving nonlinear least squares problems. Bull. Lviv Univ. Ser. Appl. Math. Inform. 2017, 25, 38–48 (in Ukrainian).
  18. Ulm S. On generalized divided differences, I. Izv. Akad. Nauk ESSR Ser. Fiz. Mat. Tekh. Nauk 1967, 16 (1), 13–26 (in Russian).
  19. Ulm S. On generalized divided differences, II. Izv. Akad. Nauk ESSR Ser. Fiz. Mat. Tekh. Nauk 1967, 16 (2), 146–156 (in Russian).
  20. Wang X. Convergence of Newton’s method and uniqueness of the solution of equations in Banach space. IMA J. Numer. Anal. 2000, 20 (1), 123–134. doi:10.1093/imanum/20.1.123