1 |
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.
|
2 |
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.
DOI
ScienceOn
|
3 |
I. K. Argyros, A semilocal convergence analysis for directional Newton methods, Math. Comput. 80 (2011), no. 273, 327-343.
|
4 |
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.
|
5 |
I. K. Argyros and S. Hilout, Inexact Newton methods and recurrent functions, App. Math. 37 (2010), no. 1, 113-126.
|
6 |
I. K. Argyros and S. Hilout, Weaker conditions for the convergence of Newton's method, J. Complexity 28 (2012), no. 3, 364-387.
DOI
ScienceOn
|
7 |
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.
DOI
|
8 |
I. K. Argyros and S. Hilout, On the semilocal convergence of damped Newton's method, Appl. Math. Comput. 219 (2012), no. 5, 2808-2824.
DOI
ScienceOn
|
9 |
I. K. Argyros, Y. J. Cho, and S. Hilout, Numerical Method for Equations and Its Applications, CRC Press/Taylor and Francis, New York, 2012.
|
10 |
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.
DOI
|
11 |
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.
DOI
|
12 |
R. S. Dembo, S. C. Eisenstat, and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal. 19 (1982), no. 2, 400-408.
DOI
ScienceOn
|
13 |
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.
DOI
ScienceOn
|
14 |
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.
DOI
ScienceOn
|
15 |
X. Guo, On semilocal convergence of inexact Newton method, J. Comput. Math. 25 (2007), no. 2, 231-242.
|
16 |
L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.
|
17 |
F. V. Haeseler and H. Kriete, Surgery for relaxed Newton's method, Complex Variables Theory Appl. 22 (1993), no. 1-2, 129-143.
DOI
|
18 |
B. T. Polyak, Newton-Kantorovich method and its global convergence, J. Math. Sci. (N. Y.) 133 (2006), no. 4, 1513-1523.
DOI
ScienceOn
|
19 |
A. M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York, 1966.
|
20 |
J. M. Ortega andW. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
|
21 |
A. M. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, Academic Press, Nueva York, 1973.
|
22 |
L. B. Rall, Computational Solution of Nonlinear Operator Equations, Robert E. Krieger Publishing Company, Inc., California, 1979.
|
23 |
W. Shen and C. Li, Kantorovich-type convergence criterion for inexact Newton method, Appl. Numer. Math. 59 (2009), no. 7, 1599-1611.
DOI
ScienceOn
|
24 |
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.
|
25 |
J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, New Jersey, 1964.
|
26 |
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.
|
27 |
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.
DOI
ScienceOn
|
28 |
T. J. Ypma, Historical development of the Newton-Raphson method, SIAM Rev. 37 (1995), no. 4, 531-551.
DOI
ScienceOn
|
29 |
T. J. Ypma, Local convergence of inexact Newton methods, SIAM J. Numer. Anal. 21 (1984), no. 3, 583-590.
DOI
ScienceOn
|