Some general theorems on estimates of error of optimal adaptive direct methods of solution of operator equations of type II in Hilbert space are obtained.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
N. S. Bakhvalov, Numerical Methods [in Russian], Nauka, Moscow (1973).
S. L. Sobolev, Equations of Mathematical Physics [in Russian], Hostekhizdat, Moscow (1960).
S. V. Pereverzev, “On optimal methods for specifying information in the solution of integral equations with differentiable kernels,” Ukr. Mat. Zh.,38, No. 1, 55–63 (1986).
S. V. Pereverzev, “On the optimization of methods of approximation of solutions of integral equations with differentiable kernels,” Sib. Mat. Zh.,28, No. 3, 173–183 (1987).
N. S. Kurpel', Projection-iterative Methods for the Solution of Operator Equations [in Russian], Nauk, Dumka, Kiev (1968).
L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1981).
V. M. Tikhomirov, Some Problems in Approximation Theory [in Russian], Izdat. Mosk. Univ., Moscow (1976).
A. I. Grebennikov, “The spline-approximation method and its application,” Authors Abstract of Doctoral Dissertation, Physicomathematical Sciences, Novosibirsk (1989).
A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press (1970).
G. Valnikko, A. Pedas, and P. Uba, Methods of Solution of Weakly Singular Integral Equations [in Russian], Tartus. Univ. (1984).
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 95–102, January, 1990.
About this article
Cite this article
Solodkii, S.G. Optimization of adaptive direct methods for the solution of operator equations in Hilbert space. Ukr Math J 42, 85–92 (1990). https://doi.org/10.1007/BF01066368
- Hilbert Space
- Operator Equation
- General Theorem
- Adaptive Direct Method