Main Article Content
This paper examines conditions for the convergence of generalized Newton-like methods, and estimates the speed of convergence.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
I. K. Argyros, "Newton-like methods under mild differentiability conditions with error analysis". Bull. Austral. Math. Soc. 37,2, (1987), 131-147.
J. E. Dennis, "Toward a unified convergence theory for Newton-like methods". In: Non linear functional analysis and applications (L. B. Rall, ed.), 425-472, Academic Press, New York, 1971.
T. Fujimoto, "Global asymptotic stability of nonlinear difference equations", I. Econ. Letters, 22, (1987), 247-250.
L. V. Kantorovich, & G. P. Akilov, "Functional analysis in normed spaces". Pergamon Press, New York, 1964.
J. P. LaSalle, "The stability and control of discrete processes". Springer- Verlag, New York, 1986.
K. Okuguchi, "Mathematical foundation in economical analysis". McGraw-Hill, Tokyo, 1977 (in Japanese).
K. Okuguchi, & F. Szidarovszky, "Theory of oligopoly with multi-product firms". Springer -Verlag, New York, 1990.
J. M. Ortega, & W. C. Rheinboldt,"Iterative solutions of nonlinear equations in several variables". Academic Press, New York, 1970.
E. Polak, "Computational methods in optimization: A unified approach". Academic Press, New York, 1971.
W. C. Rheinholdt, "A unified convergence theory for a class of iterative processes" SIAM J. Num. Anal. 5,(1968), 42-63.
S. Tishyadhigama, E. Polak, & R. Klessig, "A comparative study of several convergence conditions for algorithms modeled by point-to-set maps." Mathematical Programming Study, 10, (1979), 172-190.
T. Yamamoto, & X. Chen, "Convergence domains of certain iterative methods for solving nonlinear equations". Numer. Funct. Anal. & Optimiz. 10, (1 & 2), (1989), 34~48.
P. P. Zabrejko, & D. F. Nguen, "The majorant method in the theory of Newton-Kantorovich approximations and the Ptak-error estimates". Numer. Funct. Anal. & Optimiz. 9, (1987), 671-684.