Verified bounds for least squares problems and underdetermined linear systems (Q2903115)
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scientific article; zbMATH DE number 6070721
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Verified bounds for least squares problems and underdetermined linear systems |
scientific article; zbMATH DE number 6070721 |
Statements
23 August 2012
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underdetermined linear system
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normal equations
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extra-precise residual evaluation
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algorithm
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verified error bounds
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linear least squares problem
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sparse problem
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numerical experiments
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Verified bounds for least squares problems and underdetermined linear systems (English)
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Algorithms for computing verified error bounds for linear least squares problems and underdetermined linear systems are introduced. Compared to other approaches, they do not rely on normal equations and the results are applicable also for sparse problems. The decrease of the accuracy of the previously existing bounds is circumvented by using extra precision for residual evaluations and the efficiency (in terms of the accuracy and computing time) is reported in numerical experiments. The algorithms are implemented in the Matlab toolbox INTLAB.
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