Necessary and sufficient conditions of convergence of finite-dimensional approximations for \(L\)-regularized solutions of operator equations (Q2712502)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Necessary and sufficient conditions of convergence of finite-dimensional approximations for \(L\)-regularized solutions of operator equations |
scientific article |
Statements
6 May 2001
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ill-posed linear operator equations
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regularization
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\(L\)-regularized solution
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finite-difference approximation method
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integro-differential equation
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Hilbert spaces
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convergence
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Necessary and sufficient conditions of convergence of finite-dimensional approximations for \(L\)-regularized solutions of operator equations (English)
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The author considers finite-dimensional approximations for \(L\)-regularized solutions in Hilbert spaces. Necessary and sufficient conditions on independent disturbances of the operators \(A\) and \(L\) which provide the convergence of the finite-dimensional approximations are defined in Theorem 2 (the main statement of the paper). The obtained results essentially generalize previous results of the author and can be used for development of finite-difference approximation methods for solving integro-differential equations.
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