Component-wise perturbation analysis and error bounds for linear least squares solutions |
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Authors: | Å. Björck |
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Affiliation: | (1) Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden |
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Abstract: | Perturbation bounds for the linear least squares problem minx Ax –b2 corresponding tocomponent-wise perturbations in the data are derived. These bounds can be computed using a method of Hager and are often much better than the bounds derived from the standard perturbation analysis. In particular this is true for problems where the rows ofA are of widely different magnitudes. Generalizing a result by Oettli and Prager, we can use the bounds to compute a posteriori error bounds for computed least squares solutions. |
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Keywords: | 65F20 65G05 |
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