QUALIFIED ERROR ESTIMATES OF SUCCESSIVE APPROXIMATIONS IN THEORY OF ILL-POSED LINEAR PROBLEMS
Abstract
This article deals with the necessary and sufficient conditions for the operator B, ()1,Bρ= under which the Neumann series converges strongly and on the basis of these conditions, some of the error estimates for the corresponding successive approximations are presented.
About the Authors
P. P. Zabreiko
Belarusian State University
Belarus
D. Sc. (Physics and Mathematics), Professor
Belarus
D. Sc. (Physics and Mathematics), Professor
A. V. Mikhailov
Belarusian State University
Belarus
Postgraduate student
Belarus
Postgraduate student
References
1. Kantorovich L. V., Akilov G. P. Functional analysis. Moscow, Nauka Publ., 1984. 752 p. (in Russian)
2. Krasnoselski M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stecenko V. Ya. Approximate methods for solution of operator equations. Moscow, Nauka Publ., 1969. 456 p. (in Russian)
3. Koliha J. J. Power convergence and pseudoinverses of operators in Banach spaces. Journal of Mathematical Analysis and Applications, 1974, vol. 48, no. 2, pp. 446–469. doi.org/10.1016/0022-247x(74)90170-x.
4. Zabreiko P. P. Convergence domain of the step-by-step approach for linear equations. Doklady Akademii nauk BSSR [Doklady of the Academy of Sciences of the BSSR], 1985, no. 3, pp. 201–204. (in Russian)
5. Klyushin D. A., Lyashko S. I., Nomirovskii D. A., Petunin Yu. I., Semenov V. V. Generalized Solutions of Operator Equations and Extreme Elements. New York, Springer, 2012. 202 p. doi.org/10.1007/978-1-4614-0619-8.
6. Zabreiko P. P., Mikhailov A. V. M. A. Krasnoselsky’s theorem generalization to non self-conjugate operators. Doklady Natsional’noi akademii nauk Belarusi [Doklady of the National Academy of Sciences of Belarus], 2014, vol. 58, no. 2, pp. 16–21. (in Russian)
7. Zabreiko P. P., Mikhailov A. V. Convergence of successive approximations for equations with normal operator. Doklady Natsional’noi akademii nauk Belarusi [Doklady of the National Academy of Sciences of Belarus], 2015, vol. 59, no. 4, pp. 5–10. (in Russian)
8. Zabreiko P. P., Mikhailov A. V. Correctness of some classes of non self-adjoint operators. Doklady Natsional’noi akademii nauk Belarusi [Doklady of the National Academy of Sciences of Belarus], 2016, vol. 60, no. 3, pp. 35–42. (in Russian)
9. Zabrejko P. P. Error estimates for successive approximations and spectral properties of linear operators. Numerical Functional Analysis and Applications, 1990, no. 7–8, pp. 823–838. doi.org/10.1080/01630569008816404.
Review
Views: 922
Email this article 