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Stochastic conditioning of matrix functions

Gratton, Serge and Titley-Peloquin, David Stochastic conditioning of matrix functions. (2014) SIAM/ASA Journal on Uncertainty Quantification (JUQ), 2 (1). 763-783. ISSN 2166-2525

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Official URL: https://doi.org/10.1137/140973827


We investigate the sensitivity of matrix functions to random noise in their input. We propose the notion of a stochastic condition number, which determines, to first order, the sensitivity of a matrix function to random noise. We derive an upper bound on the stochastic condition number that can be estimated efficiently by using "small-sample" estimation techniques. The bound can be used to estimate the median, or any other quantile, of the error in a function's output when its input is subjected to random noise. We give numerical experiments illustrating the effectiveness of our stochastic error estimate.

Item Type:Article
Additional Information:https://epubs.siam.org/doi/abs/10.1137/140973827
HAL Id:hal-02147970
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 - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (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:
Deposited On:09 May 2019 09:39

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