Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems (Q751186)
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scientific article; zbMATH DE number 4176352
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems |
scientific article; zbMATH DE number 4176352 |
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Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems (English)
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1990
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The author considers stable methods for the approximate solution of ill- conditioned systems of linear equations by means of Phillips-Tikhonov regularization, and by means of truncated iterative methods (i.e. iterative methods that are stopped after a fixed number of steps). It is proved that these two (families of) methods are equivalent in the sense that the endresult of a method of one family can be obtained via a process from the other method with suitable smoothing- resp. iteration- matrix. This applies to overdetermined as well as underdetermined systems of linear equations.
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ill-posed problems
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overdetermined systems
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ill-conditioned systems
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Phillips-Tikhonov regularization
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truncated iterative methods
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underdetermined systems
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