Analysis of local regularization methods and formulation of suboptimal filtration method for an equation of the first kind (Q5932930)
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scientific article; zbMATH DE number 1601093
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analysis of local regularization methods and formulation of suboptimal filtration method for an equation of the first kind |
scientific article; zbMATH DE number 1601093 |
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Analysis of local regularization methods and formulation of suboptimal filtration method for an equation of the first kind (English)
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19 June 2001
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Three modifications of the local regularization method for solving equations of the first kind are analyzed. In the first (iterative) modification, new convenient formulas for limit approximations are derived. The stability of the second modification (asymptotically close to the optimal method) is analyzed. The term ``local regularization'' is discussed. In addition, a third modification of the method with a variable regularization parameter \(\alpha\) is considered. A new method of suboptimal filtration is formulated. These modifications are compared. Formulas for the error of the solution are derived. Results of numerical experiments are presented.
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Hilbert space
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ill-posed problem
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local regularization method
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stability
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suboptimal filtration
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numerical experiments
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