| Issue |
ESAIM: M2AN
Volume 53, Number 1, January–February 2019
|
|
|---|---|---|
| Page(s) | 219 - 248 | |
| DOI | https://doi.org/10.1051/m2an/2018048 | |
| Published online | 10 April 2019 | |
Nonintrusive approximation of parametrized limits of matrix power algorithms – application to matrix inverses and log-determinants
Safran Tech, Rue des Jeunes Bois, Châteaufort CS, 80112 – 78772 Magny-les-Hameaux Cedex France
* Corresponding author: fabien.casenave@safrangroup.com
Received:
22
February
2017
Accepted:
25
August
2018
We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.
Mathematics Subject Classification: 65D05 / 65D15 / 68W25
Key words: Empirical Interpolation Method / nonintrusive approximation / inverse matrix / logarithm of determinant
© EDP Sciences, SMAI 2019
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