Are linear algorithms always good for linear problems? (Q1082778)
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scientific article; zbMATH DE number 3974185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Are linear algorithms always good for linear problems? |
scientific article; zbMATH DE number 3974185 |
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Are linear algorithms always good for linear problems? (English)
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1986
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The question is, if there are linear optimal error algorithms for all linear problems. The answer is no, which is shown in this paper with a general construction, for which every linear algorithm has infinite error, but there is a mildly nonlinear algorithm with finite error, which can be made arbitrarily small if appropriate information is used. As an example the inversion of Laplace transform over a finite interval is considered, a problem arising in remote sensing.
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complexity
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information operator
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Laplace transform inversion
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linear optimal error algorithms
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mildly nonlinear algorithm
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