Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the Conditioning of the Components of a Linear Least Squares
  Solution   In this paper, we address the accuracy of the results for the overdetermined
full rank linear least squares problem. We recall theoretical results obtained
in Arioli, Baboulin and Gratton, SIMAX 29(2):413--433, 2007, on conditioning of
the least squares solution and the components of the solution when the matrix
perturbations are measured in Frobenius or spectral norms. 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
also provide fragment codes using LAPACK routines to compute the
variance-covariance matrix and the least squares conditioning and we give the
corresponding computational cost. Finally we present a small historical
numerical example that was used by Laplace in Theorie Analytique des
Probabilites, 1820, for computing the mass of Jupiter and experiments from the
space industry with real physical data.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con