This work examines the problem of ill-posed problems, which often arise in various fields of science and practice. Ill-posed problems are characterized by the lack of a unique solution, sensitivity to changes in input data, and instability of the solution. The aim of the work is to study the essence of ill-posed problems, identify the reasons for their occurrence, and consider examples from different areas of knowledge. Particular attention is paid to the theoretical aspects of ill-posed problems, such as non-uniqueness of the solution, sensitivity to input data, and uncertainty. The paper describes methods for solving ill-posed problems, including regularization, optimization, statistical, and machine learning methods. These approaches allow to deal with uncertainty and instability of the solution. The study of ill-posed problems is of great practical importance, as they often occur in real-life situations and require special methods for their solution. This research will be useful for specialists in various fields, as well as for anyone who faces the task of solving problems in their daily activities.
This work examines the problem of ill-posed problems, which often arise in various fields of science and practice. Ill-posed problems are characterized by the lack of a unique solution, sensitivity to changes in input data, and instability of the solution. The aim of the work is to study the essence of ill-posed problems, identify the reasons for their occurrence, and consider examples from different areas of knowledge. Particular attention is paid to the theoretical aspects of ill-posed problems, such as non-uniqueness of the solution, sensitivity to input data, and uncertainty. The paper describes methods for solving ill-posed problems, including regularization, optimization, statistical, and machine learning methods. These approaches allow to deal with uncertainty and instability of the solution. The study of ill-posed problems is of great practical importance, as they often occur in real-life situations and require special methods for their solution. This research will be useful for specialists in various fields, as well as for anyone who faces the task of solving problems in their daily activities.
| № | Муаллифнинг исми | Лавозими | Ташкилот номи |
|---|---|---|---|
| 1 | Bogdan A.M. | student | Fergana State University |
| № | Ҳавола номи |
|---|---|
| 1 | 1.A. N. Tikhonov, V. Ya. Arsenin “Methods for solving ill-posed problems” -Moscow “Science” 1979.2.Bakushinsky A.B., Goncharsky A.V. Incorrect tasks. Numerical methods and applications. –M.: Publishing house Mosk. University, 1989.–199 p.3.Great Soviet Encyclopedia. -Article 34622. Correct and incorrect problems P.11544.Gimadi E.H. On some mathematical models and methods for planning large-scale projects / E.Kh. Gimadi //Models and methods of optimization. Proceedings of the Institute of Mathematics. -Novosibirsk: Science. Sib. Department. -1988. -P. 89–1155.GorskyP. Introduction to the applied discipline “decision support”6.Grishchenko O.V.Management Accounting/O.V. Grishchenko // The concept of management decisions and their classification //Lecture notes. -Taganrog: TTI SFU, 2007. –69 p.7.KazievV.M.Introduction to systems analysis, synthesis and modeling. / V.M.Kaziev// Lecture13:Fundamentals of decision making and situational modeling. –M.: Internet University. –2006. -P.49-53 [Electronic resource] http://www.intuit.ru/department/expert/intsys/13/4.html8.Leonov A.S., Yagola A.G. Adaptive regulatory algorithms for solving incorrect problems / M.: Bulletin of Moscow University. -1998. -No. 2 (March-April). -P. 62-63 [Electronic resource]9.http://www.phys.msu.ru/upload/iblock/a84/98-2-62.pdf10.Leonov A.S., Yagola A.G. Optimal methods for solving ill-posed problems with source-like representable solutions / M.: Fundam. and adj. math. -1998 volume 4, issue 3. –pp. 1029–104611.Plunket L., Development and adoption of management decisions, M.: Nauka, 1984 –146 p.12.Tikhonov A.N. On the solution of ill-posed problems and the regularization method // Reports of the USSR Academy of Sciences. –1963. –151. –No. 3. –P.501-504.13.Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G. Numerical methods for solving ill-posed problems. M., 1990.14.Lavrentiev M.M., Romanov V.G., Shishatsky S.P. Ill-posed problems of mathematical physics and analysis. M., 1980.15.Vladimirov, V.S. Equations of mathematical physics / V.S. Vladimirov. -M.: Nauka, 1988. -439 p. |