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The exact condition number of the truncated singular value solution of a linear ill-posed problem

Bergou, El Houcine and Gratton, Serge and Tshimanga Ilunga, Jean The exact condition number of the truncated singular value solution of a linear ill-posed problem. (2014) SIAM Journal on Mathematical Analysis, 35 (3). 1073-1085. ISSN 0036-1410

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Official URL: https://doi.org/10.1137/120869286

Abstract

The main result of this paper is the formulation of an explicit expression for the condition number of the truncated least squares solution of $Ax=b$. This expression is given in terms of the singular values of $A$ and the Fourier coefficients of $b$. The result is derived using the notion of the Fréchet derivative together with the product norm on the data $[A,b]$ and the 2-norm on the solution. Numerical experiments are given to confirm our results by comparing them to those obtained by means of a finite difference approach.

Item Type:Article
Additional Information:https://epubs.siam.org/doi/abs/10.1137/120869286
HAL Id:hal-02147972
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Centre Européen de Recherche et Formation Avancées en Calcul Scientifique - CERFACS (FRANCE)
Laboratory name:
Funders:
Fondation Sciences et Technologies pour l’Aéoro-nautique et l ’Espace (STAE), Toulouse, France - Réseau Thématique de Recherche Avancée (RTRA)
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Deposited By: IRIT IRIT
Deposited On:09 May 2019 15:03

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