A general semilocal convergence result for Newton’s method under centered conditions for the second derivative
José Antonio Ezquerro; Daniel González; Miguel Ángel Hernández
- Volume: 47, Issue: 1, page 149-167
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] S. Amat and S. Busquier, Third-order iterative methods under Kantorovich conditions. J. Math. Anal. Appl.336 (2007) 243–261. Zbl1128.65036MR2348504
- [2] S. Amat, C. Bermúdez, S. Busquier and D. Mestiri, A family of Halley-Chebyshev iterative schemes for non-Fréechet differentiable operators. J. Comput. Appl. Math.228 (2009) 486–493. Zbl1173.65036MR2514306
- [3] I.K. Argyros, A Newton–Kantorovich theorem for equations involving m-Fréchet differentiable operators and applications in radiative transfer. J. Comput. Appl. Math.131 (2001) 149–159. Zbl0983.65069MR1835709
- [4] I.K. Argyros, An improved convergence analysis and applications for Newton-like methods in Banach space, Numer. Funct. Anal. Optim.24 (2003) 653–572. Zbl1040.47045MR2011587
- [5] I.K. Argyros, On the Newton-Kantorovich hypothesis for solving equations. J. Comput. Appl. Math.169 (2004) 315–332. Zbl1055.65066MR2072881
- [6] D.D. Bruns and J.E. Bailey, Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state. Chem. Eng. Sci.32 (1977) 257–264.
- [7] K. Deimling, Nonlinear functional analysis. Springer-Verlag, Berlin (1985). Zbl0559.47040MR787404
- [8] J.A. Ezquerro and M.A. Hernández, Generalized differentiability conditions for Newton’s method. IMA J. Numer. Anal.22 (2002) 187–205. Zbl1006.65051MR1897406
- [9] J.A. Ezquerro and M.A. Hernández, On an application of Newton’s method to nonlinear operators with ω-conditioned second derivative. BIT42 (2002) 519–530. Zbl1028.65061MR1931884
- [10] J.A. Ezquerro and M.A. Hernández, Halley’s method for operators with unbounded second derivative. Appl. Numer. Math.57 (2007) 354–360. Zbl1252.65098MR2292441
- [11] J.A. Ezquerro, D. González and M.A. Hernández, Majorizing sequences for Newton’s method from initial value problems. J. Comput. Appl. Math. (submitted). Zbl1241.65051
- [12] M. Ganesh and M.C. Joshi, Numerical solvability of Hammerstein integral equations of mixed type. IMA J. Numer. Anal.11 (1991) 21–31. Zbl0719.65093MR1089546
- [13] J.M. Gutiérrez, A new semilocal convergence theorem for Newton’s method. J. Comput. Appl. Math.79 (1997) 131–145. Zbl0872.65045MR1437974
- [14] L.V. Kantorovich, On Newton’s method for functional equations. Dokl Akad. Nauk SSSR 59 (1948) 1237–1240 (in Russian).
- [15] L.V. Kantorovich, The majorant principle and Newton’s method. Dokl. Akad. Nauk SSSR 76 (1951) 17–20 (in Russian).
- [16] L.V. Kantorovich and G.P. Akilov, Functional analysis. Pergamon Press, Oxford (1982). Zbl0484.46003MR664597
- [17] A.M. Ostrowski, Solution of equations in Euclidean and Banach spaces. London, Academic Press (1943). Zbl0304.65002MR359306
- [18] F.A. Potra and V. Pták, Sharp error bounds for Newton process. Numer. Math.34 (1980) 63–72. Zbl0434.65034MR560794
- [19] J. Rashidinia and M. Zarebnia, New approach for numerical solution of Hammerstein integral equations. Appl. Math. Comput.185 (2007) 147–154. Zbl1110.65126MR2298437
- [20] W.C. Rheinboldt, A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal.5 (1968) 42–63. Zbl0155.46701MR225468
- [21] T. Yamamoto, Convergence theorem for Newton-like methods in Banach spaces. Numer. Math.51 (1987) 545–557. Zbl0633.65049MR910864
- [22] Z. Zhang, A note on weaker convergence conditions for Newton iteration. J. Zhejiang Univ. Sci. Ed. 30 (2003) 133–135, 144 (in Chinese). Zbl1043.65075MR1973328