The use and properties of Tikhonov filter matrices (Q2706256)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The use and properties of Tikhonov filter matrices |
scientific article |
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19 March 2001
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Tikhonov filter matrices
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Tikhonov regularization
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rank-deficient
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pseudoinverse
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filter factors
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ill-posed linear systems
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least squares
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The use and properties of Tikhonov filter matrices (English)
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Tikhonov's regularized inverse \(J^\sharp\) of a matrix \(J\) is studied in connection with discrete ill-posed and rank-deficient linear problems. New perturbation identities are derived for the regularized least squares problem using filter matrices \(JJ^\sharp\), \(J^\sharp J\), \(I\)-\(JJ^\sharp\), \(I\)-\(J^\sharp J\). When the differential \(dJ\) is known then the differentials of the filter matrices are given explicitly.
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