Computing the Conditioning of the Components of a Linear Least Squares Solution
 
 
Description:  We address the accuracy of the results for the overdetermined full rank linear least squares problem. We recall theoretical results on conditioning of the least squares solution and the components of the solution. Then we define computable estimates for these condition numbers and we interpret them in terms of statistical quantities. In particular, we show that, in the classical linear statistical model, the ratio of the variance of one component of the solution by the variance of the right-hand side is exactly the condition number of this solution component when perturbations on the right-hand side are considered. We describe how to compute the variance-covariance matrix and the least squares conditioning using current libraries and we give the corresponding computational cost. Finally we present a numerical example from the space industry with real physical data.
Area(s):
Date:  2008-12-02
Start Time:   14:30
Speaker:  Marc Baboulin (CMUC/Mat. FCTUC)
Place:  5.5.
Research Groups: -Algebra and Combinatorics
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Science and Technology Foundation
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