Abstract
The convergence rate of a Krylov method such as the Generalized Conjugate Residual (GCR) [6] method, to solve a linear system \( Au= \; f,A=(a_{ij})\in \;\mathbb{R}^{m\times m},u \;\in \mathbb{R}^{m},f\in\mathbb{R}^{m}, \) decreases with increasing condition number \( k_{2}=\parallel A \parallel_{2}\parallel A^{-1} \parallel_{2} \) of the non singular matrix A.
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Acknowledgements
This work was funded by the French National Agency of Research under the contract ANR-TLOG07-011-03 LIBRAERO. The work of the second author was also supported by the région Rhône-Alpes through the cluster AUTOMOTIVE.
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Dufaud, T., Tromeur-Dervout, D. (2013). ARAS2 Preconditioning Technique for CFD Industrial Cases. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_67
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