Literature cited
B. T. Polyak, “Gradient methods for minimization of functionals,” Zh. Vychisl. Matem, i Matem. Fiz.,3, No. 4 (1963).
M. M. Vainberg, “Convergence of the steepest descent process for nonlinear equations,” SMZh,2, No. 2 (1961).
E. S. Levitin and B. T. Polyak, “Minimization methods for constrained problems,” Zh. Vychisl. Matern, i Matern. Fiz.,6, No. 5 (1966).
S. G. Mikhlin, Numerical Implementation of Variational Methods [in Russian], Nauka, Moscow (1966).
A. N. Tikhonov, “Stability of the problem of optimization of functionals,” Zh. Vychisl. Matem, i Matem. Fiz.,6, No. 4 (1966).
N. S. Smirnov, Introduction to the Theory of Nonlinear Integral Equations [in Russian], ONTI (1936).
M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations [in Russian], Gostekhizdat, Moscow (1956).
M. D. Babich and V. V. Ivanov, “Estimate of total error in solving nonlinear operator equations by simple iterations,” Zh. Vychisl. Matem. i Matem. Fiz.,7, No. 5 (1967).
I. H. Wilkinson, “Rounding errors in algebraic processes,” Her Majesty's Stationery Office, London (1963).
L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 21, No. 1, pp. 3–14, January–February, 1969.
Rights and permissions
About this article
Cite this article
Babich, M.D., Ivanov, V.V. Investigation of the total error in minimization of functionals with constraints. Ukr Math J 21, 1–10 (1969). https://doi.org/10.1007/BF01086676
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01086676