Statistical estimates for the conditioning of linear least squares problems

Marc Baboulin (1) , Serge Gratton (2, 3) , Rémi Lacroix (1) , Alan J Laub (4)

1 ParSys - LRI - Systèmes parallèles (LRI)
2 IRIT-APO - Algorithmes Parallèles et Optimisation
3 Toulouse INP - Institut National Polytechnique (Toulouse)
4 UCLA - University of California [Los Angeles]

In this paper we are interested in computing linear least squares (LLS) condition numbers to measure the numerical sensitivity of an LLS solution to perturbations in data. We propose a statistical estimate for the norm-wise condition number of an LLS solution where perturbations on data are measured using the Frobenius norm for matrices and the Euclidean norm for vectors. We also explain how condition numbers for the components of an LLS solution can be computed. We present numerical experiments that compare the statistical condition estimates with their corresponding exact values.

Mots clés: statistical condition estimation; component-wise conditioning.; componentwise conditioning; condition number; Linear least squares; component-wise conditioning

Domaines: Analyse numérique [cs.NA]

Marc Baboulin, Serge Gratton, Rémi Lacroix, Alan J Laub. Statistical estimates for the conditioning of linear least squares problems. International Conference on Parallel Processing and Applied Mathematics, Sep 2013, Warsaw, Poland. pp.124-133, ⟨10.1007/978-3-642-55224-3_13⟩. ⟨hal-01766923⟩