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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.
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