Проекційно-ітераційна реалізація явних методів варіаційного типу для розв’язання некоректних операторних рівнянь
Projection-iteration regularizing methods based on explicit variation type methods (steepest descent and minimal residual methods) are investigated for solving ill-posed linear operator equations in a Hilbert space which do not satisfy the third condition of the correctness of the problem by Hadamar...
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| Datum: | 2017 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2017
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| Schlagworte: | |
| Online Zugang: | http://journal.iasa.kpi.ua/article/view/71474 |
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| Назва журналу: | System research and information technologies |
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System research and information technologies| Zusammenfassung: | Projection-iteration regularizing methods based on explicit variation type methods (steepest descent and minimal residual methods) are investigated for solving ill-posed linear operator equations in a Hilbert space which do not satisfy the third condition of the correctness of the problem by Hadamard (stability). The proposed approach is to replace the original ill-posed equation by a sequence of simpler equations that approximate it defined in finite-dimensional subspaces of the original space. Then, only few approximations for each of the "approximate" equations are constructed using an explicit variation method, and the last of them is used as the initial approximation in the iterative process for the next "approximate" equation. The theorems on the convergence of the projection-iteration methods are proved, error estimates are obtained. The recommendations on the choice of the regularizing number of iterations are given. |
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