Abstract
A regularized version of Steffensen's method is proposed for the minimization of functions on a set in a Hilbert space defined by inequality and equality constraints. We derive conditions linking the regularization parameters and the penalty coefficient with the numerical method parameter, which ensure strong convergence of the method to the normal solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature Cited
S. Yu. Ul'm, "A generalization of Steffensen's method for the solution of nonlinear operator equations," Zh. Vychisl. Mat. Mat. Fiz.,4, No. 6, 1093–1097 (1964).
L. N. Khromova, "On one minimization method with cubic rate of convergence," Vestn. Mosk. Gos. Univ., Ser. Vychisl. Mat. Kibern., No. 3, 52–56 (1980).
F. P. Vasil'ev, Numerical Methods of Solution of Extremal Problems [in Russian], Nauka, Moscow (1980).
F. P. Vasil'ev, Methods of Solution of Extremal Problems [in Russian], Nauka, Moscow (1981).
Additional information
Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 5–9, 1985.
Rights and permissions
About this article
Cite this article
Vasil'ev, F.P. Iterative regularization of Steffensen's method. Comput Math Model 1, 1–4 (1990). https://doi.org/10.1007/BF01128302
Issue Date:
DOI: https://doi.org/10.1007/BF01128302