Extended Local Analysis of Inexact Gauss-Newton-like Method for Least Square Problems using Restricted Convergence Domains

[1] I.K. Argyros, Computational theory of iterative methods, Studies in Computational Mathematics (15), C.K. Chui and L. Wuytack (Eds.), Elsevier Publ. Co., New York, U.S.A, 2007.Search in Google Scholar

[2] I.K. Argyros, Y.J. Cho, and S. Hilout, Numerical methods for equations and its applications, CRC Press, Taylor and Francis, New York, 2012.10.1201/b12297Search in Google Scholar

[3] I.K. Argyros and S. Hilout, Weak convergence conditions for inexact Newton-type methods, Appl. Math. Comput.218, (2011), 2800-2809.10.1016/j.amc.2011.08.023Search in Google Scholar

[4] I.K. Argyros and S. Hilout, Extending the applicability of the Gauss-Newton method under average Lipschitz-type conditions, Numer. Algorithms, 58, (2011), 23-52.10.1007/s11075-011-9446-9Search in Google Scholar

[5] I.K. Argyros and S. Hilout, Weaker conditions for the convergence of Newton’s method, J. Complexity, 28, (2012), 364-387.10.1016/j.jco.2011.12.003Search in Google Scholar

[6] J. Chen, The convergence analysis of inexact Gauss-Newton methods for nonlinear problems, Comput. Optim. Appl.40, (2008), 97-118.10.1007/s10589-007-9071-7Search in Google Scholar

[7] J. Chen and W. Li, Convergence of Gauss–Newton’s method and uniqueness of the solution, Appl. Math. Comput.170, (2005), 686–705.10.1016/j.amc.2004.12.055Search in Google Scholar

[8] J. Chen and W. Li, Convergence behaviour of inexact Newton methods under weaker Lipschitz condition, J. Comput. Appl. Math.191, (2006), 143-164.10.1016/j.cam.2005.03.076Search in Google Scholar

[9] R.S. Dembo, S.C. Eisenstat, and T. Steihaus, Inexact Newton methods, SIAM J. Numer. Anal.19, (1982), 400-408.10.1137/0719025Search in Google Scholar

[10] J.E.Jr. Dennis and R.B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations (Corrected reprint of the 1983 original), Classics in Appl. Math. (16), SIAM, Philadelphia, PA, 1996.10.1137/1.9781611971200Search in Google Scholar

[11] B. Morini, Convergence behaviour of inexact Newton method, Math. Comp.61, (1999), 1605-1613.10.1090/S0025-5718-99-01135-7Search in Google Scholar

[12] J.M. Ortega and W.C. Rheinholdt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.Search in Google Scholar

[13] G.W. Stewart, On the continuity of the generalized inverse, SIAM J. Appl. Math.17, (1969), 33–45.10.1137/0117004Search in Google Scholar

[14] W.C. Rheinholdt, An adaptive continuation process for solving systems of nonlinear equations, Polish Academy of Science, Banach Ctr. Publ.3, (1977), 129-142.10.4064/-3-1-129-142Search in Google Scholar

[15] J.F. Traub, Iterative methods for the solution of equations, Prentice-Hall Series in Automatic Computation, Englewood Cliffs, N. J. 1964.Search in Google Scholar