| Autor: |
Baboulin, Marc, Gratton, Serge, Lacroix, Rémi, Laub, Alan J. |
| Přispěvatelé: |
Laboratoire de Recherche en Informatique (LRI), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Department of Mathematics [UCLA], University of California [Los Angeles] (UCLA), University of California-University of California, INRIA |
| Jazyk: |
angličtina |
| Rok vydání: |
2012 |
| Předmět: |
|
| Zdroj: |
[Research Report] RR-8065, INRIA. 2012, pp.15 |
| Popis: |
Linear least squares (LLS) is a classical linear algebra problem in scientific computing, arising for instance in many parameter estimation problems. In addition to computing efficiently LLS solutions, an important issue is to assess the numerical quality of the computed solution. The notion of conditioning provides a theoretical framework that can be used to measure the numerical sensitivity of a problem solution to perturbations in its data. We recall some results for least squares conditioning and we derive a statistical estimate for the conditioning of an LLS solution. We present numerical experiments to compare exact values and statistical estimates. We also propose performance results using new routines on top of the multicore-GPU library MAGMA. This set of routines is based on an efficient computation of the variance-covariance matrix for which, to our knowledge, there is no implementation in current public domain libraries LAPACK and ScaLAPACK. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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