참고문헌
- J. Appell, E. de Pascale, J. V. Lysenko, and P. P. Zabrejko, New results on Newton-Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18 (1997), no. 1-2, 1-17.
- I. K. Argyros, A new convergence theorem for the inexact Newton method based on assumptions involving the second Frechet derivative, Comput. Math. Appl. 37 (1999), no. 7, 109-115. https://doi.org/10.1016/S0898-1221(99)00091-7
- I. K. Argyros, A semilocal convergence analysis for directional Newton methods, Math. Comput. 80 (2011), no. 273, 327-343.
- I. K. Argyros and S. Hilout, On the convergence of inexact Newton-type methods using recurrent functions, Panamer. Math. J. 19 (2009), no. 1, 79-96.
- I. K. Argyros and S. Hilout, Inexact Newton methods and recurrent functions, App. Math. 37 (2010), no. 1, 113-126.
- I. K. Argyros and S. Hilout, Weaker conditions for the convergence of Newton's method, J. Complexity 28 (2012), no. 3, 364-387. https://doi.org/10.1016/j.jco.2011.12.003
- I. K. Argyros and S. Hilout, Estimating upper bounds on the limit pointss of majorizing sequences for Newton's method, Numer. Algor. 62 (2013), no. 1, 115-132. https://doi.org/10.1007/s11075-012-9570-1
- I. K. Argyros and S. Hilout, On the semilocal convergence of damped Newton's method, Appl. Math. Comput. 219 (2012), no. 5, 2808-2824. https://doi.org/10.1016/j.amc.2012.09.011
- I. K. Argyros, Y. J. Cho, and S. Hilout, Numerical Method for Equations and Its Applications, CRC Press/Taylor and Francis, New York, 2012.
- Z.-Z. Bai and J.-L. Dong, A modified damped Newton method for linear complementarity problems, Numer. Algorithms 42 (2006), no. 3-4, 207-228. https://doi.org/10.1007/s11075-006-9028-4
- X. J. Chen and L. Q. Li, A parameterized Newton method and a quasi-Newton method for nonsmooth equations, Comput. Optim. Appl. 3 (1994), no. 2, 157-179. https://doi.org/10.1007/BF01300972
- R. S. Dembo, S. C. Eisenstat, and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal. 19 (1982), no. 2, 400-408. https://doi.org/10.1137/0719025
- R. Fontecilla, T. Steihaug, and R. A. Tapia, A convergence theory for a class of quasi-Newton method for constrained optimization, SIAM J. Numer. Anal. 24 (1987), no. 5, 1133-1151. https://doi.org/10.1137/0724075
- B. I. Epureanu and H. S. Greenside, Fractal basins of attraction associated with a damped Newton's method, SIAM Rev. 40 (1998), no. 1, 102-109. https://doi.org/10.1137/S0036144596310033
- X. Guo, On semilocal convergence of inexact Newton method, J. Comput. Math. 25 (2007), no. 2, 231-242.
- L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.
- F. V. Haeseler and H. Kriete, Surgery for relaxed Newton's method, Complex Variables Theory Appl. 22 (1993), no. 1-2, 129-143. https://doi.org/10.1080/17476939308814653
- B. T. Polyak, Newton-Kantorovich method and its global convergence, J. Math. Sci. (N. Y.) 133 (2006), no. 4, 1513-1523. https://doi.org/10.1007/s10958-006-0066-1
- J. M. Ortega andW. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
- A. M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York, 1966.
- A. M. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, Academic Press, Nueva York, 1973.
- L. B. Rall, Computational Solution of Nonlinear Operator Equations, Robert E. Krieger Publishing Company, Inc., California, 1979.
- W. Shen and C. Li, Kantorovich-type convergence criterion for inexact Newton method, Appl. Numer. Math. 59 (2009), no. 7, 1599-1611. https://doi.org/10.1016/j.apnum.2008.11.002
- T. Steihaug, Quasi-Newton methods for large scale nonlinear problems, Ph.D Thesis, Res. Rep. 49, School of Organization and Management, Yale University, New Hacen, CT, 1980.
- J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, New Jersey, 1964.
- S. Weerakon and T. G. I. Fernando, A variant of Newton's method with accelerated third-order convergence, Appl. Math. Lett. 13 (2000), no. 8, 87-93.
- T. Yamamoto, Historical developments in convergence analysis for Newton's and Newton-like methods, J. Comput. Appl. Math. 124 (2000), no. 1-2, 1-23. https://doi.org/10.1016/S0377-0427(00)00417-9
- T. J. Ypma, Historical development of the Newton-Raphson method, SIAM Rev. 37 (1995), no. 4, 531-551. https://doi.org/10.1137/1037125
- T. J. Ypma, Local convergence of inexact Newton methods, SIAM J. Numer. Anal. 21 (1984), no. 3, 583-590. https://doi.org/10.1137/0721040
피인용 문헌
- A new tool to study real dynamics: The convergence plane vol.248, 2014, https://doi.org/10.1016/j.amc.2014.09.061
- Modifications of Newton’s method to extend the convergence domain vol.66, pp.1, 2014, https://doi.org/10.1007/s40324-014-0020-y