Regularization methods for ill-posed problems in multiple Hilbert scales (Q2888753)
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scientific article; zbMATH DE number 6042576
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regularization methods for ill-posed problems in multiple Hilbert scales |
scientific article; zbMATH DE number 6042576 |
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Regularization methods for ill-posed problems in multiple Hilbert scales (English)
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4 June 2012
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inverse problem
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ill-posed problem
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Hilbert scale
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Tikhonov regularization
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An overview of the theory of regularization methods in Hilbert scales is presented. The concept of a multiple Hilbert scale on a product space is introduced, the regularization methods on these scales are defined, first for the case of a single observation and then for the case of multiple observations. Convergence results in Hilbert scales under special conditions are proved. The orders of convergence are derived. The problem of optimal convergence is studied and the optimal orders of convergence are obtained.
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